SOLUTION: Could you please help me with this question? Thank you in advance! Find the volume AND total surface area of the shape <a rel=nofollow HREF="https://ibb.co/J5H3pGQ"><img src

Algebra ->  Surface-area -> SOLUTION: Could you please help me with this question? Thank you in advance! Find the volume AND total surface area of the shape <a rel=nofollow HREF="https://ibb.co/J5H3pGQ"><img src      Log On


   

Question 1191047: Could you please help me with this question? Thank you in advance!
Find the volume AND total surface area of the shape
IMG-8716
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you have three parts: half of the sphere (height=r=12}}}, cylinder h=12, and cone h=12
with same base
base is a circle with diameter d=2%2A12-> radius+r=12
height of each part is h=12

volume of a hemisphere is half the volume of sphere:
volume of sphere:
V=%284%2F3%29%2Ar%5E3%E2%80%8B%2Api

volume of hemisphere
V=%282%2F3%29%2Ar%5E3%E2%80%8B%2Api
V=%282%2F3%29%2A12%5E3%E2%80%8B%2Api
V=1152pi...............eq.1


cylinder:
V%5Bc%5D=r%5E2%2Api%2Ah
V%5Bc%5D=12%5E2%2Api%2A12
V%5Bc%5D=1728pi...........eq.2

cone:
V%5Bco%5D=%281%2F3%29r%5E2%2Api%2Ah
V%5Bco%5D=%281%2F3%2912%5E2%2Api%2A12
V%5Bco%5D=576pi.........eq.3

total volume of the shape

V=+1152pi%2B1728pi%2B576pi
V=+3456pi-> exact solution
V=10857.34-> approximately

surface area
of a half sphere is:
SA%5Bs%2F2%5D=%284pi%2Ar%5E2%29%2F2
SA%5Bs%2F2%5D=2pi%2Ar%5E2
SA%5Bs%2F2%5D=2pi%2A12%5E2
SA%5Bs%2F2%5D=288pi

cylinder:
SA%5Bc%5D=2r%5E2%2Api%2B2rpi%2Ah-> we do not need bases (shape is open inside)
SA%5Bc%5D=+2%2A12pi%2A12
SA%5Bc%5D=288pi

cone:
we do not need base
SA%5Bp%5D=2r%2Api%2As where s is lateral height
l=sqrt%28h%5E2%2Br%5E2%29=sqrt%2812%5E2%2B12%5E2%29=12sqrt%282%29 slant height
SA%5Bp%5D=2%2A12%2Api%2A12sqrt%282%29
SA%5Bp%5D=288sqrt%282%29%2Api

total surface area is

SA+=288pi%2B288pi%2B288sqrt%282%29%2Api

SA+=3089.107+approximately