Asolid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown.

what is the surface area of the figure? express the answer in terms of π.

96 + 64π cm2
96 + 80π cm2
96 + 112π cm2
96 + 128π cm2

The surface area of the figure is 96 + 64π ⇒ 1st answer

Step-by-step explanation:

* Lats revise how to find the surface area of the cylinder

- The surface area = lateral area + 2 × area of one base

- The lateral area = perimeter of the base × its height

* Lets solve the problem

- The figure is have cylinder

- Its diameter = 8 cm

∴ Its radius = 8 ÷ 2 = 4 cm

- Its height = 12 cm

∵ The perimeter of the semi-circle = πr

∴ The perimeter of the base = 4π cm

∵ The area of semi-circle = 1/2 πr²

∴ The area of the base = 1/2 × π × 4² = 8π cm²

* Now lets find the surface area of the half-cylinder

- SA = lateral area + 2 × area of one base + the rectangular face

∵ LA = perimeter of base × its height

∴ LA = 4π × 12 = 48π cm²

∵ The dimensions of the rectangular face are the diameter and the

   height of the cylinder

∴ The area of the rectangular face = 8 × 12 = 96 cm²

∵ The area of the two bases = 2 × 8π = 16π cm²

∴ SA = 48π + 16π + 96 = 64π + 96 cm²

* The surface area of the figure is 96 + 64π

what is all that apply?

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00