Sample QuestionsSurface 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.
A cylindrical piece of maximum volume has to be cut out of an iron cube of edge $4\ cm.$ Then, the maximum volume of the iron cylinder is:
- A
$24\pi\text{cm}^3$
- ✓
$16\pi\text{cm}^3$
- C
$32\pi\text{cm}^3$
- D
$28\pi\text{cm}^3$
Answer: B.
View full solution →If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon is:
- A
$5 : 1$
- B
$4 : 1$
- ✓
$8 : 1$
- D
$6 : 1$
Answer: C.
View full solution →The total surface area of a cube is $96\ cm^2$. The volume of the cube is:
- A
$8\ cm^3$
- B
$27\ cm^3$
- ✓
$64\ cm^3$
- D
$512\ cm^3$
Answer: C.
View full solution →Volume of a cuboid is $12\ cm^3$. The volume $($in $cm^3)$ of a cuboid whose side are doubled of the above cuboid is:
Answer: D.
View full solution →A cube whose volume is $\frac{1}{8}$ cubic centimeter is placed on top of a cube whose volume is $1\ cm^3$. The two cubes are then placed on top of a third cube whose volume is $8\ cm^3$. The height of the stacked cubes is:
- A
- B
$3\ cm$
- ✓
$3.5\ cm$
- D
$7\ cm$
Answer: C.
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: 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.
- B
Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- C
Assertion is correct but reason is false.
- D
Both 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: 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.
- B
Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- C
Assertion is correct but reason is false.
- D
Both 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 $=\pi\text{cm}^2\text{h}$
- A
Both Assertion and reason are correct and reason is correct explanation for Assertion.
- B
Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- ✓
Assertion is correct but reason is false.
- D
Both Assertions and reason are false.
Answer: C.
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: Volume of sphere $=\frac{4}{3}\pi\text{r}^3$ and it’s surface area $4\pi\text{r}^2$
Reason: If the volumes of two spheres are in the ratio $27 : 8$ then their surface area are in ratio $9 : 4$
- ✓
Both Assertion and reason are correct and reason is correct explanation for Assertion.
- B
Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- C
Assertion is correct but reason is false.
- D
Both 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: 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 $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be $6:\pi.$
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 $r.$
View full solution →If the length of the diagonal of a cube is $6\sqrt{3}\text{cm},$ then the length of the edge of the cube is $3\ cm$
View full solution →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 $0.21 m.$
View full solution →Find the amount of water displaced by a solid spherical ball of diameter $28\ cm.$
View full solution →Find the volume of a sphere whose radius is $0.63\ m.$
View full solution →Find the volume of a sphere whose radius is $7 \ cm$
View full solution →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
$i.$ radius $r\ '$ of the new sphere, and
$ii.$ ratio of $S$ and $S\ '$.
View full solution →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 $ABC$ 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
$i.$ inside surface area of the dome.
$ii.$ Volume of the air inside the dome.
View full solution →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.
A right triangle $ABC$ 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 $ABC$ 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:
$i.$ Height of the cone
$ii.$ Slant height of the cone
$iii.$ surface area of the cone.
View full solution →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 →This is the picture of an ice-cream cone.
The radius of the cone is $4\ cm$ and the height is $15\ cm$
An ice-cream seller keeps $1/4$ of it empty.
$10.$ What is the volume $($in $cm^3)$ of the empty part of the cone$?$
$A. 12π$
$B. 15π$
$C. 19π$
$D. 20π$ View full solution →A company manufactures wooden boxes. Given below is the picture of an open wooden box.
The height of the box is $25\ cm$
7. What is the surface area $($in $cm^2)$ of the box$?$
$A. 3500$
$B. 4700$
$C. 5900$
$D. 30000$
$8.$ A shopkeeper store cubes in it.
The side length of one cube is $9\ cm$
What would be the maximum number of cubes the shopkeeper can store in a box$? ($All cubes should be inside the box.$)$
$9.$ Rajan packs a football into a cubical cardboard box. The radius of the football is $11\ cm.$ Rajan keeps a margin of $1 \ cm$ from all the sides of the box while packing.
What is the side length of the cardboard box$?$
$A. 11\ cm$
$B. 20\ cm$
$C. 22\ cm$
$D. 24\ cm$ View full solution →Raghav bought this planter.
The radius of the rim is $14\ cm.$ The curved surface area of the planter is $1848\ cm^2$
$5.$ What is the height of the planter$?$
$6.$ What is the volume of the planter$?$ View full solution →This is the picture of a gas balloon illed with helium gas.
This balloon has $18$ faces that are square in shape and $8$ equilateral faces that are triangular.
$3.$ Which of the following is the net of the balloon$?$
$4.$ The side length of the square is $20\ cm.$ What is the total surface area of the balloon$?$ View full solution →Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The top of the hut is a cone with radius $4\ m$ and height $1\ m$. It is made of economical material. The loor of the tent is covered with rugs.
The total height of the tent is $4.5\ m.$ The cuboidal part of the tent is $6\ m$ long and $5\ m$ wide.
$1.$ What is the outer surface area $($in $m^2)$ of the hut$?$
$A. 77$
$B. 77+4π√17$
$C. 137+4π√17$
$D. 137+4π(4+√17)$
$2.$ The length and width of a rug used for the loor are $2.6\ m$ and $2\ m$ respectively.
What is the minimum number of rugs required to cover the loor of the tent house$?$
View full solution →