Geometric Properties : Volume and Surface Area

(36) A cylindrical tank has a radius of 6 meters and a height of 12 meters. Calculate its total surface area.

• (a) 576π m²
• (b) 432π m²
• (c) 648π m²
• (d) 720π m²

Answer

Correct Answer: (b) 432π m²
Explanation: The total surface area \( A \) of a cylindrical tank with radius \( r \) and height \( h \) is given by \( A = 2\pi r^2 + 2\pi rh \).
\[ A = 2\pi \times 6^2 + 2\pi \times 6 \times 12 = 432\pi \, m^2 \]

(37) A cone has a base radius of 7 cm and a height of 10 cm. Calculate its slant height.

• (a) 11.2 cm
• (b) 8.5 cm
• (c) 12.5 cm
• (d) 9.8 cm

Answer

Correct Answer: (a) 11.2 cm
Explanation: The slant height \( l \) of a cone with base radius \( r \) and height \( h \) can be found using the Pythagorean theorem.
\[ l = \sqrt{r^2 + h^2} = \sqrt{7^2 + 10^2} = \sqrt{149} \approx 11.2 \, cm \]

(38) A rectangular prism has dimensions of 4 cm, 6 cm, and 8 cm. Calculate its volume.

• (a) 144 cm³
• (b) 192 cm³
• (c) 216 cm³
• (d) 256 cm³

Answer

Correct Answer: (b) 192 cm³
Explanation: The volume \( V \) of a rectangular prism with dimensions \( l \), \( w \), and \( h \) is given by \( V = lwh \).
\[ V = 4 \times 6 \times 8 = 192 \, cm^3 \]

(39) A sphere has a surface area of 154π cm². Calculate its radius.

• (a) 7 cm
• (b) 8 cm
• (c) 6 cm
• (d) 9 cm

Answer

Correct Answer: (a) 7 cm
Explanation: The surface area \( S \) of a sphere with radius \( r \) is given by \( S = 4\pi r^2 \).
\[ 154\pi = 4\pi r^2 \]
\[ r^2 = \frac{154\pi}{4\pi} \]
\[ r^2 = 38.5 \]
\[ r = \sqrt{38.5} \approx 7 \, cm \]

(40) 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) 288 cm³
• (c) 324 cm³
• (d) 360 cm³

Answer

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