Question

The diagram shows a solid which is half of a cone. Calculate the total surface area of the solid.
a. ( 48 + 48$\pi$ ) $cm^{2}$
b. ( 48 + 15$\pi$ ) $cm^{2}$
c. ( 48 + 30$\pi$ ) $cm^{2}$
d. ( 24 + 15$\pi$ ) $cm^{2}$

Answer 1

Answer:

100πcm².

None of the options is correct

Step-by-step explanation:

Total surface area of a cone $S$ = $\pi r^{2}+\pi rl$

Since the diagram is half of a cone, its surface area will be $S = \frac{\pi r^{2} +\pi rl}{2}$

r = radius of the cone

l = slant height

From the diagram diameter of the cone = 16m;

r = 16/2 = 8m

l = 17m

$S = \frac{\pi (8)^{2} +\pi (8)(17)}{2}\\S = \frac{64\pi + 136\pi }{2} \\S = 32\pi + 68\pi \\S = 100\pi cm^{2}$