A hollow sphere has a volume of k cm\(^3\) and a surface area of k cm\(^2\). Calculate the diameter of the sphere.
A
3 cm
B
9 cm
C
More information needed.
D
6 cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Volume of sphere = \(\frac{4}{3}\)\pir\(^3\)
Surface area of sphere = 4\pir\(^2\)
Since volume and area = k cm\(^3\) and k cm\(^2\)
\(\frac{4}{3}\)\pir\(^3\) = 4\pir\(^2\)
\(\frac{4}{3}\)r\(^3\) = 4r\(^2\)
4\pir\(^3\) = 12\pir\(^2\)
r\(^3\) - 3r\(^2\) = 0
r\(^2\)(r - 3) = 0 ⇒ r = 3 cm
d = 2 x 3 = 6cm.
Source: Myschool Past Questions Archive (Record #75838)