This easy mark as brainiest 234 in word form

answer:

two hundred thirty four

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