Question

a right cylindrical solid is cut in half to form the figure shown. if the length is 20 cm and the diameter is 8 cm, what is the surface area?
(80π + 160) cm²
(96π + 160) cm²
320π cm²
(320π + 160) cm²

Explanation:

Step1: Find radius of the cylinder

The diameter is 8 cm, so radius $r = \frac{8}{2} = 4$ cm.

Step2: Calculate curved surface area half

Curved surface area of full cylinder is $2\pi r l$. Half of it is $\frac{1}{2} \times 2\pi r l = \pi r l$.
$\pi \times 4 \times 20 = 80\pi$ cm²

Step3: Calculate area of two semicircles

Two semicircles make one full circle: $\pi r^2 = \pi \times 4^2 = 16\pi$ cm²

Step4: Calculate area of rectangular face

The rectangle has length 20 cm and width 8 cm: $20 \times 8 = 160$ cm²

Step5: Sum all surface areas

Total surface area = $80\pi + 16\pi + 160 = 96\pi + 160$ cm²

Answer:

$(96\pi + 160)$ cm²