If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is:
Question types
Surface Areas and Volumes question types
529 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
529
Questions
8
Question groups
5
Question types
01
M.C.Q
385 Q→02Assertion (A) & Reason (B) MCQ
60 Q→03True False[1 Marks ]
10 Q→041 Marks Question
27 Q→052 Marks Questions
21 Q→063 Marks Question
13 Q→075 Marks Questions
3 Q→08Case study (4 Marks)
10 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.
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A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
The volume of a cylinder of radius r is $\frac{1}{4}$ of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?
View full solution →To make a closed hollow cone of base radius $7\ cm$ and height $24\ cm,$ the area of metal sheet required is:
View full solution →A sphere of diameter 12.6cm is melted and cast into a right circular cone of height 25.2cm. The radius of the base of the cone is:
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The volume and surface Area of a sphere are related to each other by radius.
Reason: Relation between Surface Area S and Volume V is $\text{S}^{(3)}=36\text{ p}_\text{i}\text{v}^{(2)}$
View full solution →Assertion: The volume and surface Area of a sphere are related to each other by radius.
Reason: Relation between Surface Area S and Volume V is $\text{S}^{(3)}=36\text{ p}_\text{i}\text{v}^{(2)}$
- Both Assertion and reason are correct and reason is correct explanation for Assertion.
- Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- Assertion is correct but reason is false.
- Both Assertions and reason are false.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the outer and inner diameter of a circular path is 10m and 6m respectively, then area of the path is $16\pi\text{m}^2.$
Reason: If R and r be the radius of outer and inner circular path respectively, then area of circular path $=\pi(\text{R}2-\text{r}2).$
View full solution →Assertion: If the outer and inner diameter of a circular path is 10m and 6m respectively, then area of the path is $16\pi\text{m}^2.$
Reason: If R and r be the radius of outer and inner circular path respectively, then area of circular path $=\pi(\text{R}2-\text{r}2).$
- Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- Assertion (A) is true but reason (R) is false.
- Assertion (A) is false but reason (R) is true.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A cone is solid figure.
Reason: A cone is generated when rectangular sheet is rotated about its axis.
Assertion: A cone is solid figure.
Reason: A cone is generated when rectangular sheet is rotated about its axis.
- Both Assertion and reason are correct and reason is correct explanation for Assertion.
- Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- Assertion is correct but reason is false.
- Both Assertions and reason are false.
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If a ball shape of a sphere has surface area $221.76\ cm^2$ then it’s diameter is $8.4\ cm$
Reason: If the radius of sphere be r then the surface area, $\text{S}=4\pi\text{r}^\text{2}$
Assertion: If a ball shape of a sphere has surface area $221.76\ cm^2$ then it’s diameter is $8.4\ cm$
Reason: If the radius of sphere be r then the surface area, $\text{S}=4\pi\text{r}^\text{2}$
- ✓Both Assertion and reason are correct and reason is correct explanation for Assertion.
- BBoth Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is correct but reason is false.
- DBoth Assertions and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The curved surface area of a cone base radius 3cm and height 4cm is $15\pi\text{cm}^2$
Reason: Curved surface area of a cone $=\pi\text{cm}^2\text{h}$
View full solution →Assertion: The curved surface area of a cone base radius 3cm and height 4cm is $15\pi\text{cm}^2$
Reason: Curved surface area of a cone $=\pi\text{cm}^2\text{h}$
- Both Assertion and reason are correct and reason is correct explanation for Assertion.
- Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- Assertion is correct but reason is false.
- Both Assertions and reason are false.
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 r.
If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.
How many litres of milk can a hemispherical bowl of diameter $10.5 \ cm$ hold?
View full solution →Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.
Find the amount of water displaced by a solid spherical ball of diameter 28 cm.
Find the volume of a sphere whose radius is 0.63 m.
Find the volume of a sphere whose radius is 7 cm.
Twenty$-$seven solid iron spheres, each of radius r and surface area $S$ are melted to form a sphere with surface area $S\ '$. Find the
View full solution →- radius $r\ '$ of the new sphere, and
- ratio of $S$ and $S\ '.$
Find the volume of a sphere whose surface area is $154 \ cm^2.$
View full solution →A hemispherical tank is made up of an iron sheet $1 \ cm$ thick. If the inner radius is $1\ m,$ then find the volume of the iron used to make the tank.
View full solution →The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the metal weighs 8.9 g per $cm^3$?
View full solution →A right triangle $\text{ABC}$ with slides $5 \ cm, 12 \ cm$ and $13 \ cm$ is revolved about the side $12 \ cm.$ Find the volume of the solid so obtained.
View full solution →A dome of a building is in the form of a hemisphere. From inside, it was white$-$washed at the cost of $Rs. 4989.60.$ If the cost of white$-$washing is $Rs. 20$ per square metre. Find the
View full solution →- inside surface area of the dome.
- Volume of the air inside the dome.
The diameter of the moon is approximately one-fourth the diameter of the earth. What fraction is the volume of the moon of the volume of the earth?
A heap of wheat is in the form of a cone whose diameter is $10.5 \ m$ and height is $3 \ m$. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
View full solution →A right triangle $\text{ABC}$ with its sides $5 \ cm, 12 \ cm,$ and $13 \ cm$ is revolved about the side $12 \ cm$. Find the volume of the solid so formed. If the triangle $\text{ABC}$ is revolved about side $5 \ cm,$ then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.
View full solution →The diameter of the moon is approximately one fourth the diameter of the earth. Find the ratio of their surface areas.
The volume of a right circular cone is $9856\text{ }c{{m}^{3}}$. If the diameter of the base if 28 cm, find:
View full solution →- Height of the cone
- Slant height of the cone
- Curved surface area of the cone.
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. $\left( \text{Use }\pi \text{ = 3}\text{.14} \right)$
View full solution →Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it $($see figure$)$. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as $80 \ cm, 40 \ cm$ and $20 \ cm$ respectively, then how many square sheets of paper of side $40 \ cm$ would she require?
View full solution →Raghav bought this planter.
The radius of the rim is 14 cm. The curved surface area of the planter is 1848 cm².
5. What is the height of the planter?
6. What is the volume of the planter?
Read the passage given below and answer any four questions:
Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length $4\ m$, width $2\ m$ and the height 3m as shown in the following figure.
The room was separate at the roof of the house. The dimensions of the bricks used are: $25\ cm \times 10\ cm \times 5\ cm.$
View full solution →Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length $4\ m$, width $2\ m$ and the height 3m as shown in the following figure.
The room was separate at the roof of the house. The dimensions of the bricks used are: $25\ cm \times 10\ cm \times 5\ cm.$
- Total how many bricks will be required? $(1m^3 =1000000\ cm^3):$
- $30000$
- $40000$
- $28800$
- $27000$
- How many bricks will be used on both walls along the length $($length $= 4\ m)$?
- $19200$
- $20200$
- $18800$
- $17000$
- How many bricks will be used on both walls along the width $($width $= 3\ m)$?
- $19200$
- $9600$
- $10000$
- $15000$
- What is the volume of the room?
- $24m^3$
- $12m^3$
- $20m^3$
- $15m^3$
- What is the area of the floor?
- $10m^2$
- $12m^2$
- $8m^2$
- $8m^3$
Read the Source/ Text given below and answer any four questions:
Veena planned to make a jewellery box to gift her friend Reeta on her marriage. She made the jewellery box of wood in the shape of a cuboid. The jewellery box has the dimensions as shown in the figure below. The rate of painting the exterior of the box is $Rs. 2$ per $\ cm^2$. After making the box she took help from his friends to decorate the box.
The blue colour was painted by Deepak, Black by Suresh, green by Harsh and the yellow was painted by Naresh.
View full solution →Veena planned to make a jewellery box to gift her friend Reeta on her marriage. She made the jewellery box of wood in the shape of a cuboid. The jewellery box has the dimensions as shown in the figure below. The rate of painting the exterior of the box is $Rs. 2$ per $\ cm^2$. After making the box she took help from his friends to decorate the box.
The blue colour was painted by Deepak, Black by Suresh, green by Harsh and the yellow was painted by Naresh.
- What is the volume of the box?
- $24000\ cm^3$
- $1200\ cm^3$
- $800\ cm^3$
- $600\ cm^3$
- How much area did Suresh paint?
- $24000\ cm^2$
- $1200\ cm^2$
- $800\ cm^2$
- $600\ cm^2$
- How much area did Deepak paint?
- $24000\ cm^2$
- $600\ cm^2$
- $800\ cm^2$
- $1200\ cm^2$
- What amount did Harsh charge?
- $Rs. 800$
- $Rs. 1200$
- $Rs. 1600$
- $Rs. 2000$
- What amount did Veena pay for painting:
- $Rs. 2600$
- $Rs. 5200$
- $Rs. 5000$
- $Rs. 6000$
Read the passage given below and answer these questions:
Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying $300\ m^2$ cloth with them. As shown in the figure they made the tent with height $10\ m$ and diameter $14\ m.$ The remaining cloth was used for the floor.
View full solution →Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying $300\ m^2$ cloth with them. As shown in the figure they made the tent with height $10\ m$ and diameter $14\ m.$ The remaining cloth was used for the floor.
- How much Cloth was used for the floor?
- $31.6\ m^2$
- $16\ m^2$
- $10\ m^2$
- $20\ m^2$
- What was the volume of the tent?
- $300\ m^3$
- $160\ m^3$
- $513.3\ m^3$
- $500\ m^3$
- What was the area of the floor?
- $50\ m^2$
- $100\ m^2$
- $150\ m^2$
- $154\ m^2$
- What was the total surface area of the tent?
- $400\ m^2$
- $422.4\ m^2$
- $300\ m^2$
- $400\ m^2$
- What was the latent height of the tent?
- $12\ m$
- $12.2\ m$
- $15\ m$
- $17\ m$
Read the passage given below and answer these questions:
Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius $R = 7\ cm$ and height $10\ cm.$ He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from $A$ to $B$ equal to $3.40\ cm.$
View full solution →Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius $R = 7\ cm$ and height $10\ cm.$ He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from $A$ to $B$ equal to $3.40\ cm.$
- What is the approximate radius of the sphere?
- $7\ cm$
- $5\ cm$
- $4\ cm$
- $3\ cm$
- What is the volume of the cylinder?
- $700\ cm^3$
- $500\ cm^3$
- $1540\ cm^3$
- $2000\ cm^3$
- What is the volume of the sphere?
- $700\ cm^3$
- $600\ cm^3$
- $500\ cm^3$
- $523.8\ cm^3$
- How many litres water can be filled in the full container? $($ Take $1$ litre $= 1000\ cm^3):$
- $1.50$
- $1.44$
- $1.54$
- $2$
- What is the surface area of the sphere?
- $314.3\ m^2$
- $300\ m^2$
- $400\ m^2$
- $350\ m^2$
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