What is the surface area of the cylinder, in terms of π, if the height of the cylinder is increased by 1 cm?
Responses
A 62π
62π cm 2
B 66π
66π cm 2
C 68π
68π cm 2
D 72π
The correct answer is C) 68π cm^2.
The formula for the surface area of a cylinder is given by:
SA = 2πr(r + h),
where r is the radius of the base and h is the height of the cylinder.
If the height is increased by 1 cm, the new height would be h + 1.
Therefore, the new surface area would be:
SA = 2πr(r + h + 1)
= 2πr(r + h) + 2πr
= 2πr(r + h) + 2πr(1)
= 2πr(r + h) + 2πr.
Since 2πr(r + h) is the original surface area, we can express the new surface area as:
SA = SA + 2πr (since 2πr(1) = 2πr)
= 2πr(r + h) + 2πr
= SA + π(2r(r + h)).
Therefore, the new surface area in terms of π is 68π cm^2.