Question

The lateral area of a cylinder is 325 pi inch^2. The radius is 13 in. Find the surface area and volume. Please show all work!!!

Answer 1

Answer:

Surface area =  663π in².
Volume = (676/3)π in² ≈ 225.33 π in²

Explanation:


1) We know the radius and the lateral area.

2) With the radius you can find the areas of the top and the bottom.

For that, you use the formula: 

area of the top = area of the bottom = π r² 


∴ π (13 in)² = 169π in² (each)


3) Then, the surface area is the sum of the lateral area and the two bases (top and bottom)

surface area = lateral area + bottom area + top area = 325π in² + 2×169π in² = 663π in².

3) You  can also find the height of the cylinder.

Use the formula: lateral area = 2π r h


∴ h = lateral area / [2 π r]

⇒ h = 325 π / [ 2π (13) ] = 12.5 in


4) With  the height you can find the volume.

Use the formula: V = (4/3) π r³ 

∴ V = (4/3) π (13 in)³ = (676/3)π in² ≈ 225.33 π in²