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?
__ square units.
To find the area of the base of a right rectangular prism, we need to know the volume and the height.
The formula for the volume of a right rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
We are given that the volume of the right rectangular prism is 50 cubic units and the height is 2. Therefore, we can write the equation as 50 = lw(2).
To find the area of the base, we need to solve for l and w. We can divide both sides of the equation by 2 to isolate lw, giving us the equation 25 = lw.
Since we only know the volume and height, we cannot determine the exact values of l and w. However, we can find the possible pairs of l and w that satisfy the equation 25 = lw.
Multiples of 25 that are possible pairs for l and w are:
(1, 25)
(5, 5)
(25, 1)
Therefore, the possible areas of the base are:
For the pair (1, 25), the area of the base is 1 square unit.
For the pair (5, 5), the area of the base is 5 square units.
For the pair (25, 1), the area of the base is 25 square units.
So the area of the base can be 1 square unit, 5 square units, or 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?
Since we know the volume is 1,000 cubic units, the height is 10 units, and the length is 20 units, we can use the formula for the volume of a right rectangular prism:
V = lwh
Substituting the given values:
1,000 = 20w(10)
To find the width, we can rearrange the equation and solve for w:
1,000 = 200w
Dividing both sides by 200:
w = 1,000 / 200
w = 5
Therefore, the width of the right rectangular prism is 5 units.
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.
The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
We are given that the volume of the rectangular prism is 50 cubic feet and the height is 4 feet. Therefore, we can write the equation as 50 = lwh.
To find the area of the base, we need to solve for l and w. We can divide both sides of the equation by 4w to isolate l, giving us the equation 50/(4w) = lh.
Simplifying the equation, we have 12.5/w = lh.
We can rewrite this equation as w = 12.5/lh.
Since we only know the volume and height, we cannot determine the exact values of l and w. However, we can find the possible values of w that satisfy the equation 50 = lwh.
Let's assume l = 5 and h = 4. Substituting these values into the equation w = 12.5/lh, we have w = 12.5 / (5 * 4) = 12.5 / 20 = 0.625 feet.
Therefore, when the volume is 50 cubic feet and the height is 4 feet, the area of the base is 0.625 square feet.
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?
The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
We are given that the volume of the rectangular prism is 162,000 cubic centimeters, the height is 40 cm, and the length is 90 cm. Therefore, we can write the equation as 162,000 = 90w(40).
To find the width, we can rearrange the equation and solve for w:
162,000 = 3,600w
Dividing both sides by 3,600:
w = 162,000 / 3,600
w = 45
Therefore, the width of the rectangular prism is 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?
__ ft.^3
The volume of a right rectangular prism is given by the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the length is 7.5 feet, the width is 5 feet, and the height is 3 feet. Plugging these values into the formula, we have:
V = 7.5 * 5 * 3
Simplifying, we get:
V = 37.5 ft³
Therefore, the volume of the container is 37.5 cubic feet.