Question

A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi.(1 point)

339.12 square centimeters
339.12 square centimeters

1,356.48 square centimeters
1,356.48 square centimeters

452.16 square centimeters
452.16 square centimeters

197.82 square centimeters

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To calculate the surface area of the cone-shaped spyglass, we'll need to find the area of the circular base and the lateral surface area, or the area of the cone's slanted side.

The area of the base can be calculated using the formula for the area of a circle (A = πr²), where r is the radius.

The lateral surface area (LSA) of a cone can be calculated using the formula LSA = πrℓ, where r is the radius and ℓ is the slant height.

Given that the radius r is 6 cm and the slant height ℓ is 18 cm, let's calculate these areas:

Base area:
A_base = πr²
A_base = 3.14 × 6²
A_base = 3.14 × 36
A_base = 113.04 cm²

Lateral surface area:
LSA = πrℓ
LSA = 3.14 × 6 × 18
LSA = 3.14 × 108
LSA = 339.12 cm²

Now, add the base area and the lateral surface area together to find the total surface area of the spyglass:

Total surface area = A_base + LSA
Total surface area = 113.04 cm² + 339.12 cm²
Total surface area = 452.16 cm²

So, the surface area of the spyglass is 452.16 square centimeters.