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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.

76π square inches.

Step-by-step explanation:

The surface area of the shape consist of 3 parts: the circular base, the cylindrical base, and the cone base. So the total surface area will be given by:

Total Surface Area = Area of Circle + Surface Area of Cylindrical Base + Surface Area of Cone.

Area of Circle = π*r^2.

Surface Area of Cylinder (without base) = 2*π*r*h.

Surface Area of Cone (without base) = π*r*sqrt(r^2 + h^2).

Therefore, total area is given by:

Total Surface Area = π*r^2 + 2*π*r*h + π*r*sqrt(r^2 + h^2).

Substitute radius = 4 inches, height of cylinder = 5 inches and height of cone = 3 inches in the above formula.

Total Surface Area = π*4^2 + 2*π*4*5 + π*4*sqrt(4^2 + 3^2).

Total Surface Area = 16π + 40π+ 20π.

Total Surface Area = 76π square inches!!!

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step-by-step explanation: