Geometric Properties : Volume and Surface Area

(21) A cylindrical pipe has a radius of 5 cm and a height of 20 cm. Calculate its volume.

• (a) 250π cm³
• (b) 500π cm³
• (c) 1000π cm³
• (d) 1250π cm³

Answer

Correct Answer: (c) 1000π cm³
Explanation: The volume \( V \) of a cylindrical pipe with radius \( r \) and height \( h \) is given by \( V = \pi r^2 h \).
\[ V = \pi \times 5^2 \times 20 = 1000\pi \, cm^3 \]

(22) A cube has a surface area of 96 cm². What is the length of one side of the cube?

• (a) 4 cm
• (b) 2 cm
• (c) 6 cm
• (d) 8 cm

Answer

Correct Answer: (b) 2 cm
Explanation: The surface area \( S \) of a cube with side length \( a \) is \( S = 6a^2 \).
\[ 96 = 6a^2 \]
\[ a^2 = 16 \]
\[ a = 4 \, cm \]

(23) A sphere has a radius of 10 cm. Calculate its volume.

• (a) 2000π cm³
• (b) 2500π cm³
• (c) 4000π cm³
• (d) 5000π cm³

Answer

Correct Answer: (c) 4000π cm³
Explanation: The volume \( V \) of a sphere with radius \( r \) is given by \( V = \frac{4}{3}\pi r^3 \).
\[ V = \frac{4}{3}\pi \times 10^3 = 4000\pi \, cm^3 \]

(24) A triangular pyramid has a base with sides of length 9 cm each and a height of 12 cm. Calculate its volume.

• (a) 216 cm³
• (b) 324 cm³
• (c) 432 cm³
• (d) 288 cm³

Answer

Correct Answer: (b) 324 cm³
Explanation: The volume \( V \) of a triangular pyramid with base area \( B \) and height \( h \) is given by \( V = \frac{1}{3}Bh \).
\[ B = \frac{1}{2} \times 9 \times 12 = 54 \, cm^2 \]
\[ V = \frac{1}{3} \times 54 \times 12 = 324 \, cm^3 \]

(25) A rectangular box has dimensions 6 cm, 4 cm, and 3 cm. What is the total surface area of the box?

• (a) 96 cm²
• (b) 108 cm²
• (c) 120 cm²
• (d) 132 cm²

Answer

Correct Answer: (d) 132 cm²
Explanation: The total surface area \( A \) of a rectangular box with dimensions \( l \), \( w \), and \( h \) is given by \( A = 2lw + 2wh + 2lh \).
\[ A = 2 \times 6 \times 4 + 2 \times 4 \times 3 + 2 \times 6 \times 3 = 132 \, cm^2 \]