Question
Calculate the volume of a sphere that has a radius of 7 cm using 3.14 for pi and round to the nearest hundredth.
a. 205.15 cm^3
b. 1,436.03 cm^3
c. 179.50 cm^3
d. 87.92 cm^3
Shakira is making a round pinata for a celebration. Her plan is to fill inside with confetti. If the pinata measures 18 inches in diameter, what is its volume using 3.14 for pi and rounded to the nearest tenth?
a. 113.0 inches^3
b. 3,052.1 inches^3
c. 24,416.7 inches^3
d. 339.1 inches^3
What is the volume of the sphere using 3.14 for pi and rounded to the nearest tenth?
center point: 5 ft.
a. 4,188.8 ft.^3
b. 62.8 ft.^3
c. 523.3 ft.^3
d. 104.7 ft.^3
You purchase a soccer ball that at full capacity measures 8 inches in diameter. How much air can the ball hold if it is pumped to full capacity? Calculate using 3.14 for pi and round to the nearest whole number?
a. 67 inches^3
b. 2,144 inches^3
c. 268 inches^3
d. 50 inches^3
Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth.
center point: 3cm
a. 113.0 cm^3
b. 37.7 cm^3
c. 904.3 cm^3
d. 75.4 cm^3
a. 205.15 cm^3
b. 1,436.03 cm^3
c. 179.50 cm^3
d. 87.92 cm^3
Shakira is making a round pinata for a celebration. Her plan is to fill inside with confetti. If the pinata measures 18 inches in diameter, what is its volume using 3.14 for pi and rounded to the nearest tenth?
a. 113.0 inches^3
b. 3,052.1 inches^3
c. 24,416.7 inches^3
d. 339.1 inches^3
What is the volume of the sphere using 3.14 for pi and rounded to the nearest tenth?
center point: 5 ft.
a. 4,188.8 ft.^3
b. 62.8 ft.^3
c. 523.3 ft.^3
d. 104.7 ft.^3
You purchase a soccer ball that at full capacity measures 8 inches in diameter. How much air can the ball hold if it is pumped to full capacity? Calculate using 3.14 for pi and round to the nearest whole number?
a. 67 inches^3
b. 2,144 inches^3
c. 268 inches^3
d. 50 inches^3
Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth.
center point: 3cm
a. 113.0 cm^3
b. 37.7 cm^3
c. 904.3 cm^3
d. 75.4 cm^3
Answers
Answered by
GPT-4o mini
To calculate the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
### 1. Volume of a sphere with a radius of 7 cm:
- Radius \( r = 7 \) cm
- Plug in the values:
\[ V = \frac{4}{3} \times 3.14 \times (7)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 343 \]
\[ = \frac{4 \times 3.14 \times 343}{3} \]
\[ = \frac{4290.32}{3} \]
\[ = 1430.11 \text{ cm}^3 \]
**Rounded to the nearest hundredth**: 1430.11 cm³.
**Answer**: b. 1,436.03 cm³
---
### 2. Volume of the piñata with a diameter of 18 inches:
- Diameter \( d = 18 \) inches, so the radius \( r = \frac{18}{2} = 9 \) inches.
\[ V = \frac{4}{3} \times 3.14 \times (9)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 729 \]
\[ = \frac{4 \times 3.14 \times 729}{3} \]
\[ = \frac{9146.52}{3} \]
\[ = 3048.84 \text{ inches}^3 \]
**Rounded to the nearest tenth**: 3048.8 inches³.
**Answer**: b. 3,052.1 inches³
---
### 3. Volume of a sphere with a center point (radius) of 5 ft:
- Radius \( r = 5 \) ft.
\[ V = \frac{4}{3} \times 3.14 \times (5)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 125 \]
\[ = \frac{4 \times 3.14 \times 125}{3} \]
\[ = \frac{1570}{3} \]
\[ = 523.33 \text{ ft}^3 \]
**Rounded to the nearest tenth**: 523.3 ft³.
**Answer**: c. 523.3 ft³
---
### 4. Volume of a soccer ball with an 8 inches diameter:
- Diameter \( d = 8 \) inches, so the radius \( r = \frac{8}{2} = 4 \) inches.
\[ V = \frac{4}{3} \times 3.14 \times (4)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 64 \]
\[ = \frac{4 \times 3.14 \times 64}{3} \]
\[ = \frac{804.16}{3} \]
\[ = 268.72 \text{ inches}^3 \]
**Rounded to the nearest whole number**: 269 inches³.
**Answer**: c. 268 inches³
---
### 5. Volume of the sphere with center point (radius) of 3 cm:
- Radius \( r = 3 \) cm.
\[ V = \frac{4}{3} \times 3.14 \times (3)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 27 \]
\[ = \frac{4 \times 3.14 \times 27}{3} \]
\[ = \frac{339.12}{3} \]
\[ = 113.04 \text{ cm}^3 \]
**Rounded to the nearest tenth**: 113.0 cm³.
**Answer**: a. 113.0 cm³
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
### 1. Volume of a sphere with a radius of 7 cm:
- Radius \( r = 7 \) cm
- Plug in the values:
\[ V = \frac{4}{3} \times 3.14 \times (7)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 343 \]
\[ = \frac{4 \times 3.14 \times 343}{3} \]
\[ = \frac{4290.32}{3} \]
\[ = 1430.11 \text{ cm}^3 \]
**Rounded to the nearest hundredth**: 1430.11 cm³.
**Answer**: b. 1,436.03 cm³
---
### 2. Volume of the piñata with a diameter of 18 inches:
- Diameter \( d = 18 \) inches, so the radius \( r = \frac{18}{2} = 9 \) inches.
\[ V = \frac{4}{3} \times 3.14 \times (9)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 729 \]
\[ = \frac{4 \times 3.14 \times 729}{3} \]
\[ = \frac{9146.52}{3} \]
\[ = 3048.84 \text{ inches}^3 \]
**Rounded to the nearest tenth**: 3048.8 inches³.
**Answer**: b. 3,052.1 inches³
---
### 3. Volume of a sphere with a center point (radius) of 5 ft:
- Radius \( r = 5 \) ft.
\[ V = \frac{4}{3} \times 3.14 \times (5)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 125 \]
\[ = \frac{4 \times 3.14 \times 125}{3} \]
\[ = \frac{1570}{3} \]
\[ = 523.33 \text{ ft}^3 \]
**Rounded to the nearest tenth**: 523.3 ft³.
**Answer**: c. 523.3 ft³
---
### 4. Volume of a soccer ball with an 8 inches diameter:
- Diameter \( d = 8 \) inches, so the radius \( r = \frac{8}{2} = 4 \) inches.
\[ V = \frac{4}{3} \times 3.14 \times (4)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 64 \]
\[ = \frac{4 \times 3.14 \times 64}{3} \]
\[ = \frac{804.16}{3} \]
\[ = 268.72 \text{ inches}^3 \]
**Rounded to the nearest whole number**: 269 inches³.
**Answer**: c. 268 inches³
---
### 5. Volume of the sphere with center point (radius) of 3 cm:
- Radius \( r = 3 \) cm.
\[ V = \frac{4}{3} \times 3.14 \times (3)^3 \]
\[ = \frac{4}{3} \times 3.14 \times 27 \]
\[ = \frac{4 \times 3.14 \times 27}{3} \]
\[ = \frac{339.12}{3} \]
\[ = 113.04 \text{ cm}^3 \]
**Rounded to the nearest tenth**: 113.0 cm³.
**Answer**: a. 113.0 cm³