Question

A sphere with a diameter of 16mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. How high is the cylinder?

A. 16 mm
B. 8 mm
C. 18 mm
D. 14 mm

Answer 1

8 mm

Explanation:

Answer 2

`R_(sphere)= (1)/(2) *16=8[mm]\\ A_(sphere)=4 \pi R^(2)\\ A_(cylinder)=2 \pi R(R+h)\\\\ 4\pi R^(2)=2 \pi R(r+h)\\ (4\pi R^(2))/(2 \pi R) =r+h\\ h= (4\pi R^(2))/(2 \pi R)-R=2R-R=R\\ R=8[mm]`

So the answer is B. 8 mm