A firework rocket consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. The diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in, while the height of the cone is 3 in. Calculate the surface area of the rocket. Leave your answer in terms of π. 184π sq. in. 76π sq. in. 168π sq. in. 88π sq. in.

Step-by-step explanation:

The surface area of the cone would be the sum of the lateral surface area of the cone and the total surface area of the cylinder (one side open)

Lateral surface area of cone = πrl

Diameter of cone = 8 in

Radius, r = 8/2 = 4 in

height of cone = 3 in

To find the slant height, l, we would apply Pythagoras theorem. Thus

l² = 4² + 3² = 25

l = √25 = 5 in

Lateral surface area of cone = π × 4 × 5 = 20π

Formula for total surface area of cylinder required(one side open) is

2πrh + πr²

From the information given,

Height of cylinder, h = 5 in

Radius of cylinder = radius of cone = 4 in

Total surface area = (2 × π × 4 × 5) + (π × 4²) = 40π + 16 π = 56π

The surface area of the rocket = 20π + 56π = 76π sq. in