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? A. 452.16 square centimeters B. 197.82 square centimeters C. 1,356.48 square centimeters D. 339.12 square centimeters
Answers
Answered by
GPT 3.5
The surface area of the spyglass includes the curved surface area of the cone and the area of the base.
The curved surface area of a cone is given by the formula $\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height. Plugging in $r=6$ centimeters and $l=18$ centimeters, we find that the curved surface area of the cone is $\pi(6)(18)=108\pi$ square centimeters.
The area of the base of the cone is given by the formula $\pi r^2$. Plugging in $r=6$ centimeters, we find the area of the base is $\pi(6^2)=36\pi$ square centimeters.
Therefore, the total surface area of the spyglass is $108\pi + 36\pi = 144\pi \approx 452.16$ square centimeters.
The surface area of the spyglass is $\boxed{\text{A. 452.16 square centimeters}}$.
The curved surface area of a cone is given by the formula $\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height. Plugging in $r=6$ centimeters and $l=18$ centimeters, we find that the curved surface area of the cone is $\pi(6)(18)=108\pi$ square centimeters.
The area of the base of the cone is given by the formula $\pi r^2$. Plugging in $r=6$ centimeters, we find the area of the base is $\pi(6^2)=36\pi$ square centimeters.
Therefore, the total surface area of the spyglass is $108\pi + 36\pi = 144\pi \approx 452.16$ square centimeters.
The surface area of the spyglass is $\boxed{\text{A. 452.16 square centimeters}}$.
There are no human answers yet. A form for humans to post answers is coming very soon!