#15 i Find the surface area and the volume of the sphere. Round your answers to the nearest hundredth. C = 30T ft The surface area is about square feet and the volume is about cubic feet. 8 10 11 12 Previous 9 13 14 16 15 17 Next Type here to search 1 O II C H
#15 i Find the surface area and the volume of the sphere. Round your answers to the nearest hundredth. C = 30T ft The surface area is about square feet and the volume is about cubic feet. 8 10 11 12 Previous 9 13 14 16 15 17 Next Type here to search 1 O II C H
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Find the Surface Area and Volume of a Sphere**
**Problem #15**
*Task:* Find the surface area and the volume of the sphere. Round your answers to the nearest hundredth.
**Given Data:**
- Circumference (C) of the sphere is 30π ft.
**Expression:**
The surface area is about __________ square feet and the volume is about __________ cubic feet.
---
### **Diagram Explanation:**
The image depicts a sphere colored in light blue, with a horizontal dashed line indicating the circumference. The circumference (C) is labeled as 30π ft. There is a dot in the center of the sphere representing the center point, indicating a cross-sectional view of the sphere where the circumference measurement is taken.
---
**Instructions:**
1. Use the circumference formula for a sphere to find the radius:
\[
C = 2\pi r \\
\Rightarrow 30\pi = 2\pi r \\
\Rightarrow r = \frac{30\pi}{2\pi} \\
\Rightarrow r = 15 \, \text{ft}
\]
2. Calculate the surface area using the formula for the surface area of a sphere:
\[
\text{Surface Area} = 4\pi r^2 \\
\Rightarrow \text{Surface Area} = 4\pi (15)^2 \\
\Rightarrow \text{Surface Area} = 4\pi (225) \\
\Rightarrow \text{Surface Area} = 900\pi \\
\Rightarrow \text{Surface Area} \approx 900 \times 3.14 = 2826 \, \text{square feet}
\]
3. Calculate the volume using the formula for the volume of a sphere:
\[
\text{Volume} = \frac{4}{3}\pi r^3 \\
\Rightarrow \text{Volume} = \frac{4}{3}\pi (15)^3 \\
\Rightarrow \text{Volume} = \frac{4}{3}\pi (3375) \\
\Rightarrow \text{Volume} = 4500\pi \\
\Rightarrow \text{Volume} \approx 4500 \times 3.14 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e7bbe56-6e0f-4e60-be65-bd82ac2b3970%2F5661e232-0969-4cc8-bca4-aa82d9fe47f7%2Fr4zpaa9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Surface Area and Volume of a Sphere**
**Problem #15**
*Task:* Find the surface area and the volume of the sphere. Round your answers to the nearest hundredth.
**Given Data:**
- Circumference (C) of the sphere is 30π ft.
**Expression:**
The surface area is about __________ square feet and the volume is about __________ cubic feet.
---
### **Diagram Explanation:**
The image depicts a sphere colored in light blue, with a horizontal dashed line indicating the circumference. The circumference (C) is labeled as 30π ft. There is a dot in the center of the sphere representing the center point, indicating a cross-sectional view of the sphere where the circumference measurement is taken.
---
**Instructions:**
1. Use the circumference formula for a sphere to find the radius:
\[
C = 2\pi r \\
\Rightarrow 30\pi = 2\pi r \\
\Rightarrow r = \frac{30\pi}{2\pi} \\
\Rightarrow r = 15 \, \text{ft}
\]
2. Calculate the surface area using the formula for the surface area of a sphere:
\[
\text{Surface Area} = 4\pi r^2 \\
\Rightarrow \text{Surface Area} = 4\pi (15)^2 \\
\Rightarrow \text{Surface Area} = 4\pi (225) \\
\Rightarrow \text{Surface Area} = 900\pi \\
\Rightarrow \text{Surface Area} \approx 900 \times 3.14 = 2826 \, \text{square feet}
\]
3. Calculate the volume using the formula for the volume of a sphere:
\[
\text{Volume} = \frac{4}{3}\pi r^3 \\
\Rightarrow \text{Volume} = \frac{4}{3}\pi (15)^3 \\
\Rightarrow \text{Volume} = \frac{4}{3}\pi (3375) \\
\Rightarrow \text{Volume} = 4500\pi \\
\Rightarrow \text{Volume} \approx 4500 \times 3.14 =
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