Mathematics, 17.07.2019 02:10 kaylakk5

Afirework 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.

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Answer from: jazzhands16

The surface area of the rocket is 76π inches² ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- A firework rocket consists of a cone stacked on top of a cylinder

- The radii of the cone and the cylinder are equal

∴ Their bases are equal

- The diameter of the cylindrical base of the rocket is 8 inches

∴ The radius of the cylinder = 8 ÷ 2 = 4 inches

- The height of the cylinder is 5 inches

- The height of the cone is 3 inches

- The surface area of the rocket is the sum of the lateral area of the

cylinder , area of one base of the cylinder and the lateral area of

the cone

∵ The lateral are of the cylinder = perimeter of its base × its height

∵ The base of the cylinder is circle

∵ The perimeter of the circle (circumference) = 2πr

∵ r = 4 and h = 5

∴ The lateral area of the cylinder = 2π(4)(5) = 40π inches²

- Lets calculate the area of the base of the cylinder

∵ The area of the circle = πr²

∴ The area of the circle = π(4)² = 16π inches²

- To find the lateral area of the cone you must find the slant height l

∵ The slant height of the cone = √ (r² + h²) , where r is the radius of

the base of the cone and h is the height of the cone

∵ r = 4 and h = 3

∴ l = √(4² + 3²) = √(16 + 9) = √25 = 5 inches

∵ The lateral area of the cone = 1/2 Cl , where C is the circumference

of the base and l is the slant height

∵ C = 2πr

∴ C = 2π(4) = 8π

∵ l = 5

∴ The lateral area of the cone = 1/2 (8π)(5) = 20π inches²

- Lets find the surface area of the rocket

∵ The S.A of the rocket = L.A of the cylinder + A of the base of the

cylinder + L.A of the cone

∵ L.A of the cylinder = 40π inches²

∵ A of the base of the cylinder = 16π inches²

∵ L.A of the cone = 20π inches²

∴ The S.A = 40π + 16π + 20π = 76π inches²

* The surface area of the rocket is 76π inches²

Answer from: Quest

false

step-by-step explanation:

whenever we assume a point on a plane then according to geometry it will definitely have 2 dimensions and if it assumed in space then it will have 3 dimensions.

Answer from: Quest

true

step-by-step explanation:

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