Question

A company is choosing between two tanks for mixing chemicals. Both tanks have the same price so the company plans to choose the one that can hold the

most chemicals the first tank is conical with a diameter of 10 feet and a height of 15 feet the second tank is a hemisphere with a radius of 5.5 feet which tank should they choose? How many more gallons to the nearest gallon will that tank hold?

Answer 1

find volume
volumecone=(1/3)(h)(pi)(r^2)

hemisphere is just a half sphere aka, 1/2 times volume of sphere so
hemisphere=(1/2)(4/3)(pi)(r^3)

fnd their volumes don't evaluate the true value till end, leav pi as pi
(or use pi key for graphing or scientific calculators)


cone
d/2=r
10/2=r=5
h=15
V=(1/3)(15)(pi)(5^2)
V=(5)(pi)(25)
V=125pi

hemisphere
V=(1/2)(4/3)(pi)(5.5^3)
V=(4/6)(pi)(166.375)
V=110.91666666666666666pi

which is bigger
125pi or 110.916666666666666666pi
125 pi
by how much?
125pi-110.91666666666666pi=14.08333333333pi
aprox pi=3.14
14.08333333*3.14=44.2217
rond
44

answer is CONICAL will hold 44 cubic feet more