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

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

Answer from: Quest

0.85% : )

step-by-step explanation:

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Afirework rocket consists of a cone stacked on top of a cylinder, where the radii of the cone and th...

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