Question

Please show the steps taken to complete the problems:

Volume of a Cylinder: 34m diameter and 27m height
Use 3.14 for Pi.

Find the surface area of the cone. 8in. diameter and 7in. height.

Find the Lateral area of the square pyramid: 8in. base and 22in. slant height(?)

Answer 1

Volume cylinder = 24501.42 m³

The surface area of the cone = 151.5 in²

The lateral area of the square pyramid = 352 in²

Explanation:

∵ The volume of the cylinder = area base × height

∵ Its base is a circle

∴ V = πr² × h = 3.14 × (34/2)² × 27 = 24501.42 m³

∵ The surface area of the cone = 1/2 perimeter base × Slant height + area base

∵ Its base is a circle

∴ S.A = (1/2) × 2πr × l + πr²

∵ The slant height =
`\sqrt{7^(2)+((8)/(2))^(2)} =√(65)`

∴ S.A = 3.14 × (8/2) × √65 + 3.14 × (8/2)² = 151.5 in²

∵ The lateral area of the square pyramid = 1/2 perimeter base × slant height

∵ Its base is a square

∴ L.A = 1/2 × (8 × 4) × 22 = 352 in²