Answer:
1. A = 96π units squared
V = 96π units cubed
2. A = 90π units squared
V = 100π units cubed
Explanation:
1. We need to find the surface area first. Use the given formula and the given dimensions:
A = πr² + πrl, where r is the radius and l is the slant height
r = 6
l = 10
Plug these values in:
A = πr² + πrl = π * 6² + π * 6 * 10 = 36π + 60π = 96π units squared
The volume is denoted by: V = (1/3)πr²h, where r is the radius and h is the height. We know r = 6 and h = 8, so:
V = (1/3)πr²h
V = (1/3)π * 6² * 8 = 96π units cubed
2. Again, use the surface area formula: A = πr² + πrl and the given dimensions. We're given that the radius is r = 5 and the height is 12, so by the Pythagorean Theorem, the slant height is √(5² + 12²) = √13² = 13. Then:
A = πr² + πrl
A = π * 5² + π * 5 * 13 = 90π units squared
Now for volume:
V = (1/3)πr²h
V = (1/3)π * 5² * 12 = 100π units cubed