Question

A right circular cylinder has all of its dimensions multiplied by four. How is its surface area affected?

Answer 1

The formula for the surface area of a right circular cylinder is:\[SA _{1}=2\pi r^2+2 \pi rh\]The variables in the formula are r = radius and h = height. If we multiplied these by 4, that is 4r and 4h, and let's see what the new surface are becomes.\[SA _{2}=2 \pi (4r)^2+2 \pi (4r)(4h)=32\pi r^2+16 \pi r h\]If we subtract the initial surface area from the new increased surface area, we get:\[SA _{2}-SA _{1}=(32 \pi r^2 + 16 \pi rh)-(2 \pi r^2 +2 \pi r h)=30 \pi r^2+14\pi rh\]From this we conclude when the dimensions (height and radius) are multiplied by 4 of such a cylinder, the surface area increases by 3pir^2 + 14pirh.

@wildflower1234

Answer 2

yh....i think he is right...