Question

PLEASE HELP!!! The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi. Thank you!

Answer 1

We can separate this solid into two pieces: a cylinder and a cone. I will be finding the surface area's separately, then adding them together in the end.

Cylinder: The formula for the surface area of a cylinder is 2πrh+2πr². HOWEVER, since the cone and cylinder are connected, they don't count as part of the surface area, we don't need the 2 in 2πr². Therefore, the formula is 2πrh+πr². The radius, or r, is 10 cm. The height, or h, is 16 cm. We use those numbers and plug it in the formula:

2πrh+πr²

2π(10)(16)+π(10)²

320π+100π

420π cm²

Cone: The surface area of the cone without its base is πrL where r is the radius (10) and L is the slant length (13)

π·10·13 = 130π cm²

Total: We add the total SA of the cylinder and the cone together to find the total: 420π+130π=550π=550·3.14 ≈ 1727 cm²