Question

The height of a right circular cylinder is three times its radius. If the curved surface area of the right circular cylinder is 3696 cm², then the volume of the cylinder is equal to (taking ∏ = 22/7):

• A. 25,992 cm³
• B. 25,972 cm³
• C. 25,892 cm³
• D. 25,872 cm³

Answer 1

Answer:

D. 25,872 cm³

For a cylinder:

• $Curved Surface Area (CSA) = (2\pi r h)$

• $Volume = (\pi r^2 h)$

Given: (h = 3r), CSA = 3696 cm²,$(\pi = \frac{22}{7})$

Use CSA

• $2\pi r h = 3696$
  

Substitute (h = 3r):
$2\pi r (3r) = 3696$
$6\pi r^2 = 3696$
$6 \times \frac{22}{7} \times r^2 = 3696$
$\frac{132}{7} r^2 = 3696$
$r^2 = \frac{3696 \times 7}{132} = 196$

$r = 14 \text{ cm}$

Find volume

$V = \pi r^2 h = \pi r^2 (3r) = 3\pi r^3$
$= 3 \times \frac{22}{7} \times 14^3$
$= 3 \times \frac{22}{7} \times 2744$
$= 3 \times 22 \times 392 = 25872$

Final Answer: 25872 cm³