Sample QuestionsVolume and Surface Area questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The total surface area of a cube is $96 \mathrm{~cm}^2$. The volume of the cube is:
- A
$8 \mathrm{~cm}^3$
- B
$27 \mathrm{~cm}^3$
- ✓
$64 \mathrm{~cm}^3$
- D
$512 \mathrm{~cm}^3$
Answer: C.
View full solution →The volume of a right circular cone of height $24\ cm$ is $1232 \mathrm{~cm}^3$. Its curved surface area is:
- A
$1254 \mathrm{~cm}^2$
- B
$704 \mathrm{~cm}^2$
- ✓
$550 \mathrm{~cm}^2$
- D
$462 \mathrm{~cm}^2$
Answer: C.
View full solution →The diameter of the base of a cylinder is $6\ cm$ and its height is $14\ cm.$ The volume of the cylinder is:
- A
$198 \mathrm{~cm}^3$
- ✓
$396 \mathrm{~cm}^3$
- C
$495 \mathrm{~cm}^3$
- D
$297 \mathrm{~cm}^3$
Answer: B.
View full solution →The volume of a cube is $512 \mathrm{\sim cm}^3$. Its total surface area is:
- A
$256 \mathrm{\sim cm}^2$
- ✓
$384 \mathrm{\sim cm}^2$
- C
$512 \mathrm{\sim cm}^2$
- D
$64 \mathrm{~cm}^2$
Answer: B.
View full solution →The height of a cylinder is $14 \ cm$ and its curved surface area is $264 \mathrm{~cm}^2$. The volume of the cylinder is:
- A
$308 \mathrm{~cm}^3$
- ✓
$396 \mathrm{~cm}^3$
- C
$1232 \mathrm{~cm}^3$
- D
$1848 \mathrm{~cm}^3$
Answer: B.
View full solution →The pillars of a temple are cylindrically shaped. Each pillar has a circular base of radius $20\ cm$ and height 10m. How much concreate mixture would be required to build $14$ such pillars?
View full solution →Find the length of the longest pole that can be put in a room of dimension $(10\ m \times 10\ m \times 5\ m).$
View full solution →The outer diameter of a spherical shell is $12\ cm$ and its inner diameter is $8\ cm$. Find the volume of metal contained in the shell. Also, find its outer surface area. $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
View full solution →The surface area of sphere is $(576\pi)\text{cm}^2.$ Find its volume.$\big(\text{Take}\ \pi=\frac{22}{7}\big).$
View full solution →A solid metallic cuboid of dimensions $(9\ m \times 8\ m \times 2\ m)$ is melted and recast into solid cubes of edge $2\ m$. Find the number of cubes so formed.
View full solution →In a water heating system, there is a cylindrical pipe of length $28m$ and diameter $5\ cm.$ Find the total radiating surface in the system.
View full solution →A circus tent is cylindrical to a height of $3$ metres and conical above it. If its diameter is $105m$ and the slant height of the conical portion is $53m,$ calculate the length of the canvas 5m wide to make the required tent. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
View full solution →How many litres of water flows out of a pipe having an area of cross section of $5 cm^2$ in $1$ minute, if the speed of water in the pipe is $30 cm / sec$ ?
View full solution →A spherical ball of radius $3\ cm$ is melted and recast into three spherical balls. The radii of two of these balls are $1.5\ cm$ and $2\ cm.$ Find the radius of the third ball.
View full solution →The lateral surface area of a cylinder is $94.2\ cm^2$ and its height is $5\ cm \big($Take$\ \pi=3.14\big)$. Find:
$i.$ The radius of its base.
$ii.$ Its volume.
View full solution →If $1cm^3$ of case iron weighs $21g$, find the weight of a cast iron pipe of length $1\ m$ with a bore of $3\ cm$ in which the thickness of the metal is $1\ cm.$
View full solution →The diameter of a cylinder is $28\ cm$ and its height is $40\ cm$. Find the curved surface, total surface area and the volume of the cylinder.
View full solution →A heap of wheat is in the form of a cone of diameter $9\ m$ and height $3.5\ m$. Find its volume. How much canvas cloth is required to just cover the heap? $\big(\text{Use}\ \pi = 3.14\big).$
View full solution →How many cubic centimetres of iron are there in an open box whose external dimension are $36\ cm, 25\ cm$ and $16.5\ cm$, the iron being $1.5\ cm$ thick throughout? If $1cm^3$ of iron weighs $15g$, find the weight of the empty box in kilograms.
View full solution →A cloth having an area of $165\ m^2$ is shaped into the form of a conical tent of radius $5\ m$. $\Big($Use$\ \pi=\frac{22}{7}\Big).$
$i.$ How many students can sit in the tent if a student, on an average, occupies $\frac{5}{7}\text{m}^2$ on the ground?
$ii.$ Find the volume of the cone.
View full solution →Find the capacity of a closed rectangular cistern whose length is $8\ m$, breadth $6\ m$ and depth $2.5\ m$. Also, find the area of the iron sheet required to make the cistern.
View full solution →Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are: Length $= 24\ m$, breadth $= 25\ cm$ and height $= 6\ m$
View full solution →It is required to make a closed cylindrical tank of height $1\ m$ and base diameter $140\ cm$ from a metal sheet. How many square metres of the sheet are required for the same?
View full solution →A cylindrical water tank of diameter $1.4m$ and height $2.1m$ is being fed by a pipe of diameter $3.5cm$ through which water flows at the rate of $2m$ per second. In how much time will the tank be filled?
View full solution →A man uses a piece of canvas having an area of $551\ m^2$, to make a conical tent of base radius $7\ m$ . Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately $1\ m^2$, find the volume of the tent that can be made with it. (Use $\left.\pi=\frac{22}{7}\right)$.
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