The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5cm, then height of the cone is:
- A10cm
- ✓15cm
- C18cm
- D24cm
Answer: B.
View full solution →Question types
Surface Areas and Volumes question types
365 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
365
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8
Question groups
5
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01
M.C.Q (1 Marks)
74 Q→02Assertion (A) & Reason (B) MCQ
6 Q→03Fill In The Blanks[1 Marks ]
18 Q→041 Marks Question
24 Q→052 Marks Questions
18 Q→063 Marks Question
144 Q→075 Marks Questions
73 Q→08Case study (4 Marks)
8 Q→Sample Questions
Surface Areas and Volumes questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If two solid-hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is:
- ✓$4\pi\text{r}^2$
- B$6\pi\text{r}^2$
- C$3\pi\text{r}^2$
- D$8\pi\text{r}^2$
Answer: A.
View full solution →The diameters of two circular ends of the bucket are 44cm and 24cm. The height of the bucket is 35cm. The capacity of the bucket is:
- ✓32.7 litres
- B33.7 litres
- C34.7 litres
- D31.7 litres
Answer: A.
View full solution →The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is:
- A$3\pi\text{r}^2$
- ✓$\frac{\pi\text{r}^3}{3}$
- C$\frac{\pi\text{r}^2}{3}$
- D$3\pi\text{r}^3$
Answer: B.
View full solution →A reservoir is in the shape of a frustum of a right circular cone. It is $8m$ across at the top and $4m$ across at the bottom. If it is $6m$ deep, then its capacity is :
- ✓$176 m^3$
- B$196 m^3$
- C$200 m^3$
- D$110 m^3$
Answer: A.
View full solution →Statement-1 (A): If volumes of two spheres are in the ratio $125: 64$, then their surface areas are in the ratio $25: 16$
Statement-2 $(R)$ : If volumes of two spheres are $V_1, V_2$ and their surface areas are $S_1, S_2$ respectively, then $\frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$.
Statement-2 $(R)$ : If volumes of two spheres are $V_1, V_2$ and their surface areas are $S_1, S_2$ respectively, then $\frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): $\Lambda$ conical bessel of base radius 5 cm and height 24 cm is full of water. If the turter is ampited intert eylimitrical nessel of internal radius 10 cm . then the water level rises by 2 cm .
Statement-2 (R): Volumes of a cylinder and a cone of hase radius $r$ and height $h$ are given bu $V_1=\pi r^2 h$ and $V_2=\frac{1}{3} \pi r^2 h$.
Statement-2 (R): Volumes of a cylinder and a cone of hase radius $r$ and height $h$ are given bu $V_1=\pi r^2 h$ and $V_2=\frac{1}{3} \pi r^2 h$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If a cylinder, a cone and a hemisphere are of equal bases and have the same height, then the volume of the cylinder is equal to the sum of the volumes of cone and the hemisphere.
Statement-2 (R): If a cylinder, a cone and a hemisphere are of equal base and have the same height, then their volumes are in the ratio 3 : 1 : 2.
Statement-2 (R): If a cylinder, a cone and a hemisphere are of equal base and have the same height, then their volumes are in the ratio 3 : 1 : 2.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If the volumes of two cubes are in the ratio $V_1: V_2$, then their surface areas are in the ratio $V_1^{2 / 3}: V_2^{2 / 3}$.
Slatement-2 (R): If surface areas of two cubes are in the ratio $S_1: S_2$, then their volumes are in the ratio $S_1^{3 / 2}: S_2^{3 / 2}$.
Slatement-2 (R): If surface areas of two cubes are in the ratio $S_1: S_2$, then their volumes are in the ratio $S_1^{3 / 2}: S_2^{3 / 2}$.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A). If two metallic right circular cones of equal height and base radii 3 cm and 4 cm are melted recast into a solid sphere radius 5 cm, then the cones are of height 20 cm each.
Statement-2 (R): If two right circular cones of same height h and base radii $r_1, r_2$ are melted and recast into a solid sphere of radius r, then $h=\frac{4 r^2}{r_1+r_2}$
Statement-2 (R): If two right circular cones of same height h and base radii $r_1, r_2$ are melted and recast into a solid sphere of radius r, then $h=\frac{4 r^2}{r_1+r_2}$
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: C.
View full solution →If a marble of radius 2.1 cm is put into a cylindrical cup, full of water, of radius 5 cm and height 6 cm, then the volume of water that flows out of the cup is ____________ .
A solid cylinder of radius rand height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is ____________ .
A sloid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is ____________ .
If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the solid so formed is ____________ .
A shuttle cock used for playing badminton has the shape of the combination of ____________ and ____________ .
Three solid spheres of radii 3, 4 and 5cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
A solid piece of metal in the form of a cuboid of dimensions 11 cm x 7 cm x 7 cm is melted to form a number of a solid spheres of radii $\frac{7}{2}$ cm each. Find the value of n.
View full solution →A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.
Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
A cylindrical bucket 28cm in diameter and 72cm high is full of water. The water is emptied into a rectangular tank 66cm long and 28cm wide. Find the height of the water level in the tank.
A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter 21m and length 5m. Find the least height of the tank that will serve the purpose.
A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?
$25$ circular plates, each of radius $10.5 \ cm$ and thickness $1.6 \ cm$, are placed one above the other to form a solid circular cylinder.
Find the curved surface area and the volume of the cylinder so formed.
View full solution →Find the curved surface area and the volume of the cylinder so formed.
A solid metallic sphere of radius 5.6cm is melted and solid cones each of radius 2.8cm and height 3.2cm are made. Find the number of such cones formed.
If the heights of two right circular cones are in the ratio $1 : 2$ and the perimeters of their bases are in the ratio $3 : 4$, what is the ratio of their volumes?
View full solution →A well of diameter 3m is dug $14\ m$ deep. The earth taken out of it has been spread evenly all around it to a width of $4\ m$ to form an embankment. Find the height of the embankment.
View full solution →A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3m and its height is 3.5m?
What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
The height of a solid cylinder is $15\ cm$ and the diameter of its base is $7\ cm$. Two equal conical holes each of radius $3\ cm$, and height $4\ cm$ are cut off. Find the volume of the remaining solid.
View full solution →The $\frac{3}{4}\text{th}$ part of a conical vessel of internal radius 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height of water in cylindrical vessel.
View full solution →An icecream cone full of icecream having radius 5cm and height 10cm as shown’in the figure. Calculate the volume of icecream, provided that its $\frac{1}{6}$ parts is left unfilled with icecream.
View full solution →The internal and external diameters of a hollow hemispherical vessel are 21cm and 25.2cm respectively. The cost of painting $1cm^2$ of the surface is 10 paise. Find the total cost to paint the vessel all over.
View full solution →In the given figure, from the top of a solid cone of height 12cm and base radius 6cm, a cone of height 4cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.$\Big(\text{use}\ \pi=\frac{22}{7}\text{and}\sqrt{5}=2.236\Big).$
View full solution →A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $\frac{14}{3}\text{m}$ and the diameter of hemisphere is 3.5m. Calculate the volume and the internal surface area of the solid.
View full solution →Temper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 mL milk is packed in a cuboidal container of dimensions 15 cm x 8 cm x 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm x 32 cm x 15 сm.
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.
OR
(b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the Figure) hold?
500 mL milk is packed in a cuboidal container of dimensions 15 cm x 8 cm x 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm x 32 cm x 15 сm.
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.
OR
(b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the Figure) hold?
The word 'circus' has same root as 'circle. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.
A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m.
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.
OR
(b) Find total volume of air inside an empty tent.
A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m.
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.
OR
(b) Find total volume of air inside an empty tent.
In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm.
(i) Find the area of the base of the cylindrical cup.
(ii) What is the capacity of the hemispherical cup?
(iii) Find the capacity of the cylindrical cup.
(iv) What is the curved surface area of the cylindrical cup?
(i) Find the area of the base of the cylindrical cup.
(ii) What is the capacity of the hemispherical cup?
(iii) Find the capacity of the cylindrical cup.
(iv) What is the curved surface area of the cylindrical cup?
A golf ball is spherical with about 300-500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemispherical) of radius 2 mm.
(i) Find the surface area of one such dimple.&
(n) Find the volume of the material dug out to make one dimple.
(iii) Find the total surface area exposed to the surroundings.
(iv) Find the volume of the golf ball
(i) Find the surface area of one such dimple.&
(n) Find the volume of the material dug out to make one dimple.
(iii) Find the total surface area exposed to the surroundings.
(iv) Find the volume of the golf ball
Mathematics teacher of a school took her 10 ^ (th) standard students to show Red Fort. It was a part of their Educational trip The teacher had interest in history as well. She narrated the facts of Red Fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also, 2 domes at the corners which are hemispherical and 7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.
(i) How much cloth material will be required to cover 2 big domes each of radius 2.5 metres?
$($ Take $\pi=22 / 7)$
(a) $75 m^2$$\quad$ (b) $78.57 m^2$$\quad$ (c) $87.47 m^2$$\quad$(d) $25.8 m^2$
(ii) Write the formula to find the volume of a cylindrical pillar.
(a) $\pi r^2 h$$\quad$ (b) $\pi r l$$\quad$ (c) $\pi r(i+r)$$\quad$ (d) $2 \pi r$
(iii) Find the lateral surface area of two pillars if height of the pillar is 7 m and radius of the base is 1.4 m.
(a) $112.3 cm^2$$\quad$ (b) $123.2 m^2$$\quad$ (c) $90 m^2$$\quad$ (d) $345.2 cm^2$
(iv) How much is the volume of a hemisphere if the radius of the base is 3.5 m?
(a) $85.9 m^3$$\quad$ (b) $80 m^3$$\quad$ (c) $98 m^2$$\quad$ (d) $89.83 m^3$
View full solution →(i) How much cloth material will be required to cover 2 big domes each of radius 2.5 metres?
$($ Take $\pi=22 / 7)$
(a) $75 m^2$$\quad$ (b) $78.57 m^2$$\quad$ (c) $87.47 m^2$$\quad$(d) $25.8 m^2$
(ii) Write the formula to find the volume of a cylindrical pillar.
(a) $\pi r^2 h$$\quad$ (b) $\pi r l$$\quad$ (c) $\pi r(i+r)$$\quad$ (d) $2 \pi r$
(iii) Find the lateral surface area of two pillars if height of the pillar is 7 m and radius of the base is 1.4 m.
(a) $112.3 cm^2$$\quad$ (b) $123.2 m^2$$\quad$ (c) $90 m^2$$\quad$ (d) $345.2 cm^2$
(iv) How much is the volume of a hemisphere if the radius of the base is 3.5 m?
(a) $85.9 m^3$$\quad$ (b) $80 m^3$$\quad$ (c) $98 m^2$$\quad$ (d) $89.83 m^3$
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