The volume of a sphere which is exactly inserted in a cube of edge 6 cm , is
- ✓$36 \pi cm^3$
- B$64 \sqrt{3} \pi cm^3$
- C$14 \pi cm^3$
- D$288 \pi cm^3$
Answer: A.
View full solution →Question types
Surface Area And Volume of Sphere [NEW] question types
109 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
109
Questions
7
Question groups
5
Question types
01
M.C.Q
27 Q→02Assertion (A) & Reason (B) MCQ
8 Q→03Fill In The Blanks[1 Marks ]
13 Q→041 Marks Question
10 Q→052 Marks Questions
21 Q→063 Marks Question
22 Q→074 Marks Questions
8 Q→Sample Questions
Surface Area And Volume of Sphere [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The volume of a cube which can be inserted exactly in a sphere of radius $\frac{3 \sqrt{3}}{2} cm$ is
- A$24 cm^3$
- ✓$27 cm^3$
- C$18 cm^3$
- D$30 cm^3$
Answer: B.
View full solution →The total surface area of a hemisphere of radius r is
- A$\pi r^2$
- B$2 \pi r^2$
- ✓$3 \pi r^2$
- D$4 \pi r^2$
Answer: C.
View full solution →The surface area of a football is $100 \pi cm^2$. The volume of air in it is
- A$\frac{200 \pi}{3} cm^3$
- B$\frac{350 \pi}{3} cm^3$
- ✓$\frac{500 \pi}{3} cm^3$
- D$\frac{400 \pi}{3} cm^3$
Answer: C.
View full solution →The ratio of the total surface area of a sphere and a hemisphere of same radius is
- A2:1
- B3:2
- C4:1
- ✓4:3
Answer: D.
View full solution →Statement-1 (A): The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter of the base are equal to the diameter of the sphere.
Statement-2 (R): If a hemisphere and a cylinder stand on equal bases and have the same height, then their volumes are in the ratio 3: 2.
Statement-2 (R): If a hemisphere and a cylinder stand on equal bases and have the same height, then their volumes are in the ratio 3: 2.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is 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 →Statement-1 (A): If the volumes of two spheres are in the ratio 27: 125, then their radii are in the ratio 3:5.
Statement-2 (R): If the volumes of two spheres are in the ratio $V_1$, $V_2$ then their radii are in the ratio $V_1^{1 / 3}: V_2^{1 / 3}$.
Statement-2 (R): If the volumes of two spheres are in the ratio $V_1$, $V_2$ then their radii are in the ratio $V_1^{1 / 3}: V_2^{1 / 3}$.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is 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 surface areas of two spheres are in the ratio $9: 25$, then their radii are in the ratio $3: 5$.
Statement-2 (R) : If surface areas of two spheres are in the ratio $S_1: S_2$, then their radii are in the ratio $\sqrt{S_1}: \sqrt{S_2}$.
Statement-2 (R) : If surface areas of two spheres are in the ratio $S_1: S_2$, then their radii are in the ratio $\sqrt{S_1}: \sqrt{S_2}$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-2
- 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 ratio of volumes of two spheres is 27 : 64, then the ratio of their surface areas is 9 : 16.
Statement-2 (R): If $V_1, V_2$ are volumes and $S_1, S_2$ are surface areas of two spheres, then
$\frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$
Statement-2 (R): If $V_1, V_2$ are volumes and $S_1, S_2$ are surface areas of two spheres, 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): If the ratio of the surface areas of two spheres is 4: 9, then the ratio of their volumes is 8: 27.
Statement-2 (R): The volumes $V_1$, $V_2$ and surface areas of two sphere are connected by the relation $\left(\frac{S_1}{S_2}\right)^3=\left(\frac{V_1}{V_2}\right)^2$.
Statement-2 (R): The volumes $V_1$, $V_2$ and surface areas of two sphere are connected by the relation $\left(\frac{S_1}{S_2}\right)^3=\left(\frac{V_1}{V_2}\right)^2$.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is 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 →The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius __________.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into. The ratio of the surface areas of the balloon in two cases is __________.
If the volume of a hemisphere is $18 \pi cm^3$, $18 \pi cm^3$,__________.
View full solution →If the volume and surface area of a sphere are numerically the same, then its radius is __________.
If the ratio of the volumes of two spheres is 8/27 then the ratio of their surface areas is __________.
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
The surface area of a sphere is 5544cm2, find its diameter.
The largest sphere is carved out of a cube of side 10.5cm. Find the volume of the sphere.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding.
If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?
How many bullets can be made out of a cube of lead, whose edge measures 22cm, each bullet being 2cm in diameter?
The radius of the internal and external surfaces of a hollow spherical shell are 3cm and 5cm respectively. If it is melted and recast into a solid cylinder of height $2\frac{2}{3}$cm. Find the diameter of the cylinder.
View full solution →The dome of a building is in the form of a hemisphere. Its radius is 63dm. Find the cost of painting it at the rate of Rs. 2 per sq m.
The diameter of the moon is approximately one-fourth of the diameter of the earth. What is the earth the volume of the moon?
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface areas.
The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 0.2cm. Find the length of the wire.
The surface area of a sphere of radius 5cm is five times the area of the curved surface of a cone of radius 4cm. Find the height of the cone.
The front compound wall of a house is decorated by wooden spheres of diameter 21cm, placed on small supports as shown in the Fig. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5cm and height 7cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
If a hollow sphere of internal and external diameters 4cm and 8cm respectively melted into a cone of base diameter 8cm, then find the height of the cone.
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16cm and its height is 15cm. Find the cost of painting the toy at Rs. 7 per 100cm2
A spherical ball of lead 3cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be $\frac{3}{2}$cm and 2cm, find the diameter of the third ball.
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