A right rectangular prism has an area of 20 square units and a height of 3 units. What is the volume? (1 point)
units cubed
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
We are given the area of the prism as 20 square units. The formula for the area of a rectangular prism is A = lw + lh + wh.
Since the height is given as 3 units, we can substitute in the values into the area formula and solve for the unknowns:
20 = lw + 3l + 3w.
To simplify the equation, we can divide both sides by 3:
20/3 = (lw + 3l + 3w)/3.
Simplifying further, we get:
20/3 = lw/3 + l + w.
Since we are looking for the volume, we use the formula V = lwh and solve for V:
V = lwh = l(20/3 - lw/3 - w).
We can factor out an l:
V = l(20/3 - w(l/3 + 1)).
Since we know the height is 3 units, we substitute h = 3:
V = 3(20/3 - w(3/3 + 1)).
Simplifying further:
V = (20 - 3w(4/3)).
V = 20 - 4w.
The volume of the prism is 20 - 4w units cubed.
A gift box is being constructed in the shape of a right rectangular prism. The base is 15 inches squared and the height is 5 inches. What will the volume of the gift box be? (1 point) In.^3
To find the volume of the gift box, we use the formula V = lwh, where l is the length, w is the width, and h is the height.
We are given the base area as 15 square inches and the height as 5 inches. We can substitute in these values into the volume formula and solve for the unknowns:
V = lwh = 15 * w * 5.
V = 75w.
The volume of the gift box will be 75w cubic inches.
What is the volume of a rectangular pyramid with a length of 32 cm, a width of 25 cm, and an altitude of 41 cm? (1 point)
• 98, 400 cm*
• 10, 933.33 cm*
• 32, 800 cm*
• 32.67 cm°
The formula for the volume of a rectangular pyramid is V = (1/3) * l * w * h, where l is the length, w is the width, and h is the altitude.
Given the length as 32 cm, the width as 25 cm, and the altitude as 41 cm, we can substitute these values into the volume formula:
V = (1/3) * 32 * 25 * 41.
V = (1/3) * 32 * 1025.
V = 34 * 1025.
V = 34,850.
The volume of the rectangular pyramid is 34,850 cubic centimeters.
A resort is building a scuba diving lagoon in the shape of an upside down pyramid. The top of the lagoon is a rectangle that is 50 feet by 20 feet, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold? (1 point)
• 8,333.33 ft. 3
• 25,000 ft.3
• 95 ft.3
• 75,000 f.3
To find the volume of the lagoon, we need to calculate the volume of a frustum, which is the portion of the pyramid between the top and bottom rectangles.
The formula for the volume of a frustum is V = (1/3) * h * (A1 + A2 + sqrt(A1 * A2)), where h is the height of the frustum, A1 is the area of the top rectangle, and A2 is the area of the bottom rectangle.
Given that the top rectangle has dimensions 50 feet by 20 feet, the area of the top rectangle is A1 = 50 ft * 20 ft = 1000 ft^2.
The bottom rectangle also has the same dimensions, so the area of the bottom rectangle, A2, is also 1000 ft^2.
The height of the frustum is given as 25 feet.
Substituting these values into the volume formula:
V = (1/3) * 25 ft * (1000 ft^2 + 1000 ft^2 + sqrt(1000 ft^2 * 1000 ft^2)).
V = (1/3) * 25 ft * (2000 ft^2 + sqrt(1,000,000 ft^4)).
V ≈ (1/3) * 25 ft * (2000 ft^2 + 1000 ft^2).
V ≈ (1/3) * 25 ft * 3000 ft^2.
V ≈ 25,000 ft^3.
The lagoon holds approximately 25,000 cubic feet of water.