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Ratling [72]
3 years ago
11

A sphere and a cylinder have the same radius and height. The volume of the cylinder have the same height and radius. The volume

of the cylinder is 27pi ft. What equation gives the volume of the sphere ?
Mathematics
1 answer:
USPshnik [31]3 years ago
6 0

Step-by-step explanation:

radius of sphere, rs

radius of cylinder, rc

height of cylinder, h

given: h = rs = rc =r..eq1

volume of cylinder, vc = 27pi ft...eq2

volume of cylinder, vc = pi × rc^2 × h...eq3

volume of sphere, vs = 4/3(pi×rs^3)...eq4

subst for h & rs from eqn 1 in eqn 3...

vc = pi x r^2 x r= pi x r^3...eqn 5

subst for vc from eqn 2 in eqn 5...

=> 27 pi ft = pi x r^3

=> 27 = r^3

=> r = 3ft...eqn 6

subst for rs from eqn 1 in eqn 4

vs = 4/3 (pi x r^3)...eqn7

subst for pi x r^3 from eqn 5 in eqn 7

vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft

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Answer:

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Step-by-step explanation:

Let the number of hours the first mechanic worked = a

Let the number of hours the second mechanic worked = b

Therefore, we can write 2 equations and then solve them simultaneously:

a+b=25

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Rearranging the first equation: a=25-b

and substituting into the second equation to find b:

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1625-65b+90b=1750\\
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b=5

Now sub b=5 into the first equation to find a

a+5=25\\
a=20

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours

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