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Vadim26 [7]
3 years ago
14

A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 6 centimeters. What is the radius?

Mathematics
1 answer:
zysi [14]3 years ago
4 0
You are going to solve this in such a quick, slick way
that you will blink and not believe it.  Fasten your seat belt.

Here are the tools you'll need:

--  Volume of a cylinder  =  (pi) (radius)² (height)

--  Volume of a sphere  =  (4/3) (pi) (radius)³

Now ... the question says that your cylinder and your sphere
have the same volume.  Fine !  So you can immediately write
an equation saying that their volumes are equal.

                               (pi) (radius)² (height)  =  (4/3) (pi) (radius)³

Divide each side by pi:    (radius)² (height)  =  (4/3)       (radius)³

Divide each side by (radius)²        (height)  =  (4/3)        (radius)

Fill in the given height:                  (6 cm)    =  (4/3)      (radius)

Multiply each side by  3/4 :    (6 cm) x (3/4)  =             radius

I'm pretty sure that you can take over now and find the radius.
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