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Question

 A cylinder and a rectangular prism have the same volume and same height. The base of the prism is a square with side length 7 cm. What is the approximate radius of the cylinder? A. 4.0 cm B. 3.5 cm C. 2.2 cm D. 1.5 cm     Please explain too if possible!

Answer 1

Volume formula for both: V = Bh, B = area of base, h = height for both.

 

B_c = B_p

 

pi r^2 = 7^2

 

A circle inscribed in the 7" square would have a radius of 3.5". But that circle would have less area than the square. So the circle we need has a radius greater than 3.5".

 

The answer is A.

Answer 2

V=pi*r^2*h for a cylinder

V=l*w*h for a prism

the volumes are equal

pi*r^2*h=l*w*h

the heights are equal, so divide both sides by h

pi*r^2=l*w

l and w are both 7 cm (base is a square with side lengths 7 cm)

pi*r^2=7*7

pi*r^2=49

r^2=49/pi

r^2=49/3.14159

r^2=15.597197

take the square root of both sides

r=3.94932875 cm

3.94932875≈4, the answer is A) 4.0 cm