Geometric Properties : Volume and Surface Area

(26) A cylindrical container has a radius of 8 cm and a height of 15 cm. Calculate its total surface area.

• (a) 680π cm²
• (b) 760π cm²
• (c) 760π cm²
• (d) 840π cm²

Answer

Correct Answer: (c) 760π cm²
Explanation: The total surface area \( A \) of a cylindrical container with radius \( r \) and height \( h \) is given by \( A = 2\pi r^2 + 2\pi rh \).
\[ A = 2\pi \times 8^2 + 2\pi \times 8 \times 15 = 760\pi \, cm^2 \]

(27) A cone has a base radius of 6 cm and a slant height of 10 cm. Calculate its total surface area.

• (a) 132π cm²
• (b) 180π cm²
• (c) 240π cm²
• (d) 280π cm²

Answer

Correct Answer: (b) 180π cm²
Explanation: The total surface area \( A \) of a cone with base radius \( r \) and slant height \( l \) is given by \( A = \pi r^2 + \pi rl \).
\[ A = \pi \times 6^2 + \pi \times 6 \times 10 = 180\pi \, cm^2 \]

(28) A rectangular prism has dimensions of 5 cm, 9 cm, and 12 cm. Calculate its volume.

• (a) 450 cm³
• (b) 540 cm³
• (c) 630 cm³
• (d) 720 cm³

Answer

Correct Answer: (b) 540 cm³
Explanation: The volume \( V \) of a rectangular prism with dimensions \( l \), \( w \), and \( h \) is given by \( V = lwh \).
\[ V = 5 \times 9 \times 12 = 540 \, cm^3 \]

(29) A sphere has a surface area of 144π cm². Calculate its radius.

• (a) 3 cm
• (b) 2 cm
• (c) 4 cm
• (d) 5 cm

Answer

Correct Answer: (b) 2 cm
Explanation: The surface area \( S \) of a sphere with radius \( r \) is given by \( S = 4\pi r^2 \).
\[ 144\pi = 4\pi r^2 \]
\[ r^2 = \frac{144\pi}{4\pi} \]
\[ r^2 = 36 \]
\[ r = \sqrt{36} = 6 \, cm \]

(30) A triangular pyramid has a base with sides of length 8 cm each and a height of 10 cm. Calculate its total surface area.

• (a) 208 cm²
• (b) 224 cm²
• (c) 240 cm²
• (d) 256 cm²

Answer

Correct Answer: (c) 240 cm²
Explanation: The total surface area \( A \) of a triangular pyramid with base area \( B \) and height \( h \) is given by \( A = B + 3 \times \frac{1}{2} \times \text{base side} \times \text{slant height} \).
\[ B = \frac{1}{2} \times 8 \times 10 = 40 \, cm^2 \]
\[ A = 40 + 3 \times \frac{1}{2} \times 8 \times 10 = 240 \, cm^2 \]