A rectangular prism has a base area of 25in and a volume of 125in. If the rectangular Pyramid has a congruent base and height congruent to the prism what is the height of the Pyramid
The dimensions of the rectangular prism are:
Length x Width x Height = Base Area x Height = 25in x Height
And its volume is:
Volume = Base Area x Height = 125in
Therefore, the height of the rectangular prism is 5in.
Since the rectangular pyramid has a congruent base and height to the prism, its base area is also 25in and its volume is:
Volume = (1/3) x Base Area x Height
Substituting the values we know:
125in = (1/3) x 25in x Height
Solving for Height:
Height = 15in
Therefore, the height of the rectangular pyramid is 15in.
To find the height of the pyramid, we need to use the formula for the volume of a rectangular prism and equate it to the volume of the pyramid.
1. Given information:
- Base area of the prism: 25 in²
- Volume of the prism: 125 in³
2. Formula for the volume of a rectangular prism:
Volume = Base area x Height
3. Formula for the volume of a rectangular pyramid:
Volume = (1/3) x Base area x Height
4. Since the base area and height of the pyramid are congruent to the prism, we can set up the following equation:
(1/3) x 25 in² x h = 125 in³
5. Simplify the equation:
(1/3) x 25 in² x h = 125 in³
(1/3) x 25 in² x h = 125 in³
25/3 x h = 125
6. Solve for h (height):
Multiply both sides of the equation by 3/25:
h = (125 x 3) / 25
h = 375 / 25
h = 15
Therefore, the height of the pyramid is 15 inches.