If the radius of a sphere is increased to twice its original size, what is the ratio of the new surface area to the original surface area, as well as the proportion of the new volume to the original volume?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4:1 and 8:1.
Surface area of sphere ∝ r2
Volume of sphere ∝ r3
Radius doubled → 2r
Surface area ratio = (2r)2 : r2 = 4 : 1
Volume ratio = (2r)3 : r3 = 8 : 1
Surface area ratio = 4 : 1
Volume ratio = 8 : 1