Question
use 3.14 for pi. round to the nearest whole number. the cone has a radius of 3m and a slant height of 7 m. A.49m B.44m C.59m D.66m
Answers
GPT-4o mini
To find the surface area of a cone with a radius of 3 m and a slant height of 7 m, we can use the formula for the total surface area of a cone:
\[
\text{Surface Area} = \pi r^2 + \pi r l
\]
Where:
- \( r \) is the radius (3 m)
- \( l \) is the slant height (7 m)
1. Calculate the area of the base:
\[
\text{Base Area} = \pi r^2 = 3.14 \times (3^2) = 3.14 \times 9 = 28.26 \text{ m}^2
\]
2. Calculate the lateral surface area:
\[
\text{Lateral Area} = \pi r l = 3.14 \times 3 \times 7 = 3.14 \times 21 = 66.94 \text{ m}^2
\]
3. Add the areas together for the total surface area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} = 28.26 + 66.94 = 95.20 \text{ m}^2
\]
Now rounding to the nearest whole number:
\[
95.20 \approx 95 \text{ m}^2
\]
However, the answer choices seem to pertain to something else, likely the lateral surface area only since the options provided do not list the total surface area. The lateral surface area is:
Lateral Surface Area = 66.94 → rounded to 67.
If the answers are specifically looking for rounded lateral surface area only, and if we just take that into account and round it:
Final rounded lateral surface area: **67m²**
While that number is not listed in your answer choices, if you have made a mistake in selecting the area you need or if there is additional context or constraints, please clarify that, and I will be glad to help further. As for the choices given:
A. 49m
B. 44m
C. 59m
D. 66m
None of these would apply directly either to the total surface area or the lateral surface area based on standard definitions and calculations described.
\[
\text{Surface Area} = \pi r^2 + \pi r l
\]
Where:
- \( r \) is the radius (3 m)
- \( l \) is the slant height (7 m)
1. Calculate the area of the base:
\[
\text{Base Area} = \pi r^2 = 3.14 \times (3^2) = 3.14 \times 9 = 28.26 \text{ m}^2
\]
2. Calculate the lateral surface area:
\[
\text{Lateral Area} = \pi r l = 3.14 \times 3 \times 7 = 3.14 \times 21 = 66.94 \text{ m}^2
\]
3. Add the areas together for the total surface area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} = 28.26 + 66.94 = 95.20 \text{ m}^2
\]
Now rounding to the nearest whole number:
\[
95.20 \approx 95 \text{ m}^2
\]
However, the answer choices seem to pertain to something else, likely the lateral surface area only since the options provided do not list the total surface area. The lateral surface area is:
Lateral Surface Area = 66.94 → rounded to 67.
If the answers are specifically looking for rounded lateral surface area only, and if we just take that into account and round it:
Final rounded lateral surface area: **67m²**
While that number is not listed in your answer choices, if you have made a mistake in selecting the area you need or if there is additional context or constraints, please clarify that, and I will be glad to help further. As for the choices given:
A. 49m
B. 44m
C. 59m
D. 66m
None of these would apply directly either to the total surface area or the lateral surface area based on standard definitions and calculations described.