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. (…

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

100πcm².

None of the options is correct

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 = (\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 = (\pi (8)^(2) +\pi (8)(17))/(2)\\S = (64\pi + 136\pi )/(2) \\S = 32\pi + 68\pi \\S = 100\pi cm^(2)`