X What is the surface area for the figure below? Round to the nearest hundredth. 3 ft

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
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What is the surface area for the figure below?
### Sphere Surface Area and Volume Calculations

#### Problem 1: Surface Area Calculation

**Question:**
What is the surface area for the figure below? Round to the nearest hundredth.

![Circle with radius](image)

For this problem, a circle is shown with a radius of 3 feet. The surface area of a sphere is calculated using the formula:

\[ \text{Surface Area} = 4\pi r^2 \]

Where \( r \) is the radius of the sphere.

**Calculation:**

\[ \text{Surface Area} = 4 \times \pi \times (3)^2 \]
\[ \text{Surface Area} = 4 \times \pi \times 9 \]
\[ \text{Surface Area} = 36\pi \]
\[ \text{Surface Area} \approx 36 \times 3.14 \]
\[ \text{Surface Area} \approx 113.1 \text{ square feet} \]

The surface area is approximately \( 113.1 \text{ square feet} \).

#### Problem 2: Volume Calculation

**Question:**
What is the volume of this sphere?

![Sphere with radius](image)

For this problem, a sphere is shown with a radius of 16 meters. The volume of a sphere is calculated using the formula:

\[ \text{Volume} = \frac{4}{3}\pi r^3 \]

Where \( r \) is the radius of the sphere.

**Calculation:**

\[ \text{Volume} = \frac{4}{3} \times \pi \times (16)^3 \]
\[ \text{Volume} = \frac{4}{3} \times \pi \times 4096 \]
\[ \text{Volume} = \frac{4}{3} \times 3.14 \times 4096 \]
\[ \text{Volume} = 4.18666 \times 4096 \]
\[ \text{Volume} \approx 17157.28 \text{ cubic meters} \]

The volume is approximately \( 17157.28 \text{ cubic meters} \).
Transcribed Image Text:### Sphere Surface Area and Volume Calculations #### Problem 1: Surface Area Calculation **Question:** What is the surface area for the figure below? Round to the nearest hundredth. ![Circle with radius](image) For this problem, a circle is shown with a radius of 3 feet. The surface area of a sphere is calculated using the formula: \[ \text{Surface Area} = 4\pi r^2 \] Where \( r \) is the radius of the sphere. **Calculation:** \[ \text{Surface Area} = 4 \times \pi \times (3)^2 \] \[ \text{Surface Area} = 4 \times \pi \times 9 \] \[ \text{Surface Area} = 36\pi \] \[ \text{Surface Area} \approx 36 \times 3.14 \] \[ \text{Surface Area} \approx 113.1 \text{ square feet} \] The surface area is approximately \( 113.1 \text{ square feet} \). #### Problem 2: Volume Calculation **Question:** What is the volume of this sphere? ![Sphere with radius](image) For this problem, a sphere is shown with a radius of 16 meters. The volume of a sphere is calculated using the formula: \[ \text{Volume} = \frac{4}{3}\pi r^3 \] Where \( r \) is the radius of the sphere. **Calculation:** \[ \text{Volume} = \frac{4}{3} \times \pi \times (16)^3 \] \[ \text{Volume} = \frac{4}{3} \times \pi \times 4096 \] \[ \text{Volume} = \frac{4}{3} \times 3.14 \times 4096 \] \[ \text{Volume} = 4.18666 \times 4096 \] \[ \text{Volume} \approx 17157.28 \text{ cubic meters} \] The volume is approximately \( 17157.28 \text{ cubic meters} \).
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