Q: If a right circular cone of height $24\text{ cm}$ has a volume of $1232\text{ cm}^3$, then the total surface area of the cone is: (use $\pi = \frac{22}{7}$)

$704\text{ cm}^2$ — $V = \frac{1}{3}\pi r^2 h = 1232 \Rightarrow \frac{22}{7} \times r^2 \times 8 = 1232 \Rightarrow r = 7$. $l = \sqrt{24^2 + 7^2} = 25$. TSA = $\pi r(l+r) = \frac{22}{7} \times 7 \times 32 = 704\text{ cm}^2$.

Q: A square pyramid has a base side of 12 cm and a slant height of 10 cm. Find its lateral surface area.

$240\text{ cm}^2$ — $LSA = \frac{1}{2} \times \text{Perimeter} \times \text{Slant} = \frac{1}{2} \times 48 \times 10 = 240$.

Q: If the length, breadth, and height of a cuboid is $8\text{ cm}$, $4\text{ cm}$, and $6\text{ cm}$, respectively, then the volume of the cuboid is:

$192\text{ cm}^3$ — Volume of cuboid = $L \times B \times H = 8 \times 4 \times 6 = 192\text{ cm}^3$.

Question 1

If a right circular cone of height $24	ext{ cm}$ has a volume of $1232	ext{ cm}^3$, then the total surface area of the cone is: (use $\pi = \frac{22}{7}$)

Accepted Answer

$704	ext{ cm}^2$ — $V = \frac{1}{3}\pi r^2 h = 1232 \Rightarrow \frac{22}{7} 	imes r^2 	imes 8 = 1232 \Rightarrow r = 7$. $l = \sqrt{24^2 + 7^2} = 25$. TSA = $\pi r(l+r) = \frac{22}{7} 	imes 7 	imes 32 = 704	ext{ cm}^2$.

Question 2

A square pyramid has a base side of 12 cm and a slant height of 10 cm. Find its lateral surface area.

Accepted Answer

$240	ext{ cm}^2$ — $LSA = \frac{1}{2} 	imes 	ext{Perimeter} 	imes 	ext{Slant} = \frac{1}{2} 	imes 48 	imes 10 = 240$.

Question 3

The radii of the two cones are in the ratio of 2: 5 and their volumes are in the ratio of 3: 5. What is the ratio of their heights?

Accepted Answer

15:4 — V1/V2 = (R1/R2)² * (H1/H2) => 3/5 = (4/25) * (H1/H2). Therefore, H1/H2 = (3*25) / (5*4) = 15/4. Ratio is 15:4.

Question 4

If the length, breadth, and height of a cuboid is $8	ext{ cm}$, $4	ext{ cm}$, and $6	ext{ cm}$, respectively, then the volume of the cuboid is:

Accepted Answer

$192	ext{ cm}^3$ — Volume of cuboid = $L 	imes B 	imes H = 8 	imes 4 	imes 6 = 192	ext{ cm}^3$.

Question 5

What is the volume (in cm³) of a cylinder if the radius of the cylinder is 8 cm and the height is 14 cm? (Take π = 22/7)

Accepted Answer

2816 — Volume of cylinder = π * r^2 * h = (22/7) * 8^2 * 14 = 22 * 64 * 2 = 2816 cm³.

Mensuration 3D — Questions with Solutions

Q1. If a right circular cone of height $24\text{ cm}$ has a volume of $1232\text{ cm}^3$, then the total surface area of the cone is: (use $\pi = \frac{22}{7}$)

Q2. A square pyramid has a base side of 12 cm and a slant height of 10 cm. Find its lateral surface area.

Q3. The radii of the two cones are in the ratio of 2: 5 and their volumes are in the ratio of 3: 5. What is the ratio of their heights?

Q4. If the length, breadth, and height of a cuboid is $8\text{ cm}$, $4\text{ cm}$, and $6\text{ cm}$, respectively, then the volume of the cuboid is:

Q5. What is the volume (in cm³) of a cylinder if the radius of the cylinder is 8 cm and the height is 14 cm? (Take π = 22/7)