Question

Find the volume and surface area of the composite figure. Give your answer in terms of π.

Please give me a step-by-step explanation!!

Answer 1

V = 240π cm^3 , S= 168π cm^2

Explanation:

The given figure is a combination of hemi-sphere and a cone

Volume:

For volume

r = 6 cm

h = 8 cm

`Volume\ of\ cone = (1)/(3)\pi r^2h\\= (1)/(3)\pi (6)^2*8\\=(1)/(3)\pi *36*8\\=(288)/(3)\pi\\=96\pi cm^3 \\\\Volume\ of\ hemisphere = (2)/(3)\pi r^3\\=(2)/(3)*\pi * (6)^3\\=(2)/(3)*\pi *216\\=(432)/(3)\\=144\pi cm^3 \\\\Total\ Volume= Volume\ of\ cone + Volume\ of\ hemisphere\\= 96\pi +144\pi \\=240\pi cm^3`

Surface Area:

For this particular figure we have to consider the lateral area of the cone shape and surface area of the hemisphere

We have to find the lateral height

`l = √(r^2+h^2)\\ l = √((6)^2+(8)^2) \\l= √(36+64)\\ l = √(100)\\l = 10cm\\\\Surface\ area\ of\ cone = \pi rl\\= \pi (6)(10)\\=\pi *60\\=60 \pi\ cm^2\\\\Surface\ area\ of\ hemisphere = 2\pi r^2\\= 2 \pi * (6)\\= 2 \pi *36\\= 72 \pi\ cm^2\\\\Total\ surface\ Area = Surface\ area\ of\ cone + Surface\ area\ of \ hemisphere\\= 60 \pi + 72 \pi\\=132 \pi\ cm^2`

Hence the first option is correct ..