A crystal perfume bottle is in the shape of a square pyramid. The length of one of the sides of the base is 3 in., and the height of the bottle is 5 in. What is the volume of the bottle?(1 point)
To find the volume of the square pyramid, we can use the formula:
Volume = (1/3) * base area * height
First, we need to find the area of the base, which is a square with side length 3 in.
Base area = side length * side length = 3 in * 3 in = 9 in^2
Now, we can substitute the values into the formula:
Volume = (1/3) * 9 in^2 * 5 in
Volume = (1/3) * 45 in^2
Volume = 15 in^3
Therefore, the volume of the crystal perfume bottle is 15 cubic inches.
A "Caution Wet Floor” warning sign is in the shape of a rectangular pyramid. It is 31 in. tall and has a base whose dimensions are 12 in. by 20 in. What is the volume of the sign?(1 point)
To find the volume of the rectangular pyramid, we can use the formula:
Volume = (1/3) * base area * height
First, we need to find the area of the base, which is a rectangle with dimensions 12 in by 20 in.
Base area = length * width = 12 in * 20 in = 240 in^2
Now, we can substitute the values into the formula:
Volume = (1/3) * 240 in^2 * 31 in
Volume = (1/3) * 7440 in^2
Volume = 2480 in^3
Therefore, the volume of the "Caution Wet Floor" warning sign is 2480 cubic inches.
An illustration shows a rectangular pyramid with a length of 14 inches, a width of 6 inches, and a perpendicular height of 12 inches. The face with the length of 6 inches has a slant height of 13.89 inches. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
How many cubic inches does this rectangular pyramid contain? Round answer to the nearest whole number.
To find the volume of the rectangular pyramid, we can use the formula:
Volume = (1/3) * base area * height
First, we need to find the area of the base, which is a rectangle with dimensions 14 in by 6 in.
Base area = length * width = 14 in * 6 in = 84 in^2
Now, we can substitute the values into the formula:
Volume = (1/3) * 84 in^2 * 12 in
Volume = 336 in^2 * 12 in
Volume = 4032 in^3
Therefore, the rectangular pyramid contains 4032 cubic inches.
not an option
I apologize for the oversight. Let's recalculate the volume using the slant height provided for one of the faces.
The slant height represents the height of a right triangle formed by the height, the slant height, and half of the base, which is 3 inches (half of 6 inches).
Using the Pythagorean theorem, we can find the height of the triangle as follows:
height^2 + 3^2 = 13.89^2
height^2 + 9 = 192.972
height^2 = 192.972 - 9
height^2 = 183.972
height ≈ √183.972
height ≈ 13.56 inches
Now that we have the height of the triangular face, we can calculate the volume of the rectangular pyramid.
Volume = (1/3) * base area * height
Volume = (1/3) * (14 in * 6 in) * 13.56 in
Volume = (1/3) * 84 in^2 * 13.56 in
Volume ≈ 378.72 in^3
Rounded to the nearest whole number, the rectangular pyramid contains approximately 379 cubic inches.
Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point
To find the volume of a rectangular pyramid, we can use the formula:
Volume = (1/3) * base area * height
Given that the base is a rectangle with a length of 111 inches and a width of 111 inches, the base area is:
Base area = length * width = 111 in * 111 in = 12321 in^2
The height of the pyramid-shaped tent is 75 inches.
Now, we can substitute the values into the formula:
Volume = (1/3) * 12321 in^2 * 75 in
Volume = (1/3) * 924075 in^3
Volume = 308025 in^3
Therefore, the volume of the pyramid-shaped tent is 308025 cubic inches.