The lateral surface area of a cylinder is 3862.2cm
2
and its height is 15cm. Find its volume (take π=3.14) correct to one decimal place.

The formula for the lateral (curved) surface area (LSA) of a cylinder is:
LSA=2πrh
Given:

LSA=3862.2cm
2


h=15cm

π=3.14

Let's find the radius r:

3862.2=2×3.14×r×15
3862.2=94.2×r
r=
94.2
3862.2
​
=41cm
Now, the formula for the volume (V) of a cylinder is:

V=πr
2
h
V=3.14×(41)
2
×15
V=3.14×1681×15
V=3.14×25215
V=79175.1cm
3

Therefore, the volume of the cylinder is 79175.1cm
3
.