Question
Using the formula for the volume of a right rectangular prism, what is the area of the base when the volume is 50 cubic units and the height is 2?
(1 point)
• 100 square units
25 square units
• 75 square units
200 square units
(1 point)
• 100 square units
25 square units
• 75 square units
200 square units
Answers
GPT-4o mini
To find the area of the base of a right rectangular prism, we can use the formula for volume:
\[
V = \text{Base Area} \times \text{Height}
\]
Given that the volume \( V \) is 50 cubic units and the height \( h \) is 2 units, we can rearrange the formula to solve for the base area \( A \):
\[
A = \frac{V}{h}
\]
Now substitute the values:
\[
A = \frac{50 \text{ cubic units}}{2 \text{ units}} = 25 \text{ square units}
\]
Therefore, the area of the base is \( \boxed{25} \) square units.
\[
V = \text{Base Area} \times \text{Height}
\]
Given that the volume \( V \) is 50 cubic units and the height \( h \) is 2 units, we can rearrange the formula to solve for the base area \( A \):
\[
A = \frac{V}{h}
\]
Now substitute the values:
\[
A = \frac{50 \text{ cubic units}}{2 \text{ units}} = 25 \text{ square units}
\]
Therefore, the area of the base is \( \boxed{25} \) square units.
The volume of a right rectangular prism is 1,000, the height is 10, and the length is 20. What is the width? (1 point)
• 200,000
• 50
5
• 15
• 200,000
• 50
5
• 15
GPT-4o mini
To find the width of a right rectangular prism, we can use the formula for the volume:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Volume \( V = 1000 \) cubic units
- Height \( h = 10 \) units
- Length \( l = 20 \) units
We need to solve for the width \( w \). Rearranging the formula gives:
\[
w = \frac{V}{l \times h}
\]
Now, substitute the known values:
\[
w = \frac{1000}{20 \times 10}
\]
Calculating the denominator:
\[
20 \times 10 = 200
\]
Now, substitute this back into the formula:
\[
w = \frac{1000}{200} = 5
\]
Thus, the width of the prism is \( \boxed{5} \).
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Volume \( V = 1000 \) cubic units
- Height \( h = 10 \) units
- Length \( l = 20 \) units
We need to solve for the width \( w \). Rearranging the formula gives:
\[
w = \frac{V}{l \times h}
\]
Now, substitute the known values:
\[
w = \frac{1000}{20 \times 10}
\]
Calculating the denominator:
\[
20 \times 10 = 200
\]
Now, substitute this back into the formula:
\[
w = \frac{1000}{200} = 5
\]
Thus, the width of the prism is \( \boxed{5} \).
Monica is constructing a box in the shape of a right rectangular prism to hold grain on her farm. Use the formula for the volume of a rectangular prism to find the area of the base when the volume is 50 cubic feet and the height is 4 feet. (1 point)
• 200 ft.?
O 37.5 ft.?
• 12.5 ft.?
6.25 ft.?
• 200 ft.?
O 37.5 ft.?
• 12.5 ft.?
6.25 ft.?
GPT-4o mini
To find the area of the base of a right rectangular prism, we can use the formula for volume:
\[
V = \text{Base Area} \times \text{Height}
\]
Given:
- Volume \( V = 50 \) cubic feet
- Height \( h = 4 \) feet
We can rearrange the formula to solve for the base area \( A \):
\[
A = \frac{V}{h}
\]
Now substituting the given values:
\[
A = \frac{50 \text{ cubic feet}}{4 \text{ feet}} = 12.5 \text{ square feet}
\]
Thus, the area of the base is \( \boxed{12.5} \) ft².
\[
V = \text{Base Area} \times \text{Height}
\]
Given:
- Volume \( V = 50 \) cubic feet
- Height \( h = 4 \) feet
We can rearrange the formula to solve for the base area \( A \):
\[
A = \frac{V}{h}
\]
Now substituting the given values:
\[
A = \frac{50 \text{ cubic feet}}{4 \text{ feet}} = 12.5 \text{ square feet}
\]
Thus, the area of the base is \( \boxed{12.5} \) ft².
Hakeem is building a box in the shape of a right rectangular prism to store his toys. It has a volume of 162,000 cubic centimeters. What is the width of the box if the height is 40 cm and the length is 90 cm? (1 point)
• 45 cm
• 40 cm
• 158,400 cm
• 15 cm
• 45 cm
• 40 cm
• 158,400 cm
• 15 cm
GPT-4o mini
To find the width of a right rectangular prism, we can use the formula for the volume:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Volume \( V = 162,000 \) cubic centimeters
- Height \( h = 40 \) cm
- Length \( l = 90 \) cm
We need to solve for the width \( w \). Rearranging the formula gives:
\[
w = \frac{V}{l \times h}
\]
Now, substitute the known values:
\[
w = \frac{162,000}{90 \times 40}
\]
Calculating the denominator:
\[
90 \times 40 = 3600
\]
Now substitute this back into the formula:
\[
w = \frac{162,000}{3600} = 45
\]
Thus, the width of the box is \( \boxed{45} \) cm.
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Volume \( V = 162,000 \) cubic centimeters
- Height \( h = 40 \) cm
- Length \( l = 90 \) cm
We need to solve for the width \( w \). Rearranging the formula gives:
\[
w = \frac{V}{l \times h}
\]
Now, substitute the known values:
\[
w = \frac{162,000}{90 \times 40}
\]
Calculating the denominator:
\[
90 \times 40 = 3600
\]
Now substitute this back into the formula:
\[
w = \frac{162,000}{3600} = 45
\]
Thus, the width of the box is \( \boxed{45} \) cm.
Keysha needs to fill a container with cement. The container is in the shape of a right rectangular prism. The container has a length of 7.5 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the container? (1 point)
• 112.5 ft.3
O 1,125 ft. 3
• 15.5 ft.3
37.5 ft.3
• 112.5 ft.3
O 1,125 ft. 3
• 15.5 ft.3
37.5 ft.3
GPT-4o mini
To find the volume of a right rectangular prism, you can use the formula:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Length \( l = 7.5 \) feet
- Width \( w = 5 \) feet
- Height \( h = 3 \) feet
Now, substitute the values into the formula:
\[
V = 7.5 \times 5 \times 3
\]
First, calculate the product of the length and width:
\[
7.5 \times 5 = 37.5
\]
Next, multiply this result by the height:
\[
37.5 \times 3 = 112.5
\]
Thus, the volume of the container is \( \boxed{112.5} \, \text{ft}^3 \).
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Length \( l = 7.5 \) feet
- Width \( w = 5 \) feet
- Height \( h = 3 \) feet
Now, substitute the values into the formula:
\[
V = 7.5 \times 5 \times 3
\]
First, calculate the product of the length and width:
\[
7.5 \times 5 = 37.5
\]
Next, multiply this result by the height:
\[
37.5 \times 3 = 112.5
\]
Thus, the volume of the container is \( \boxed{112.5} \, \text{ft}^3 \).