the area of the base of a triangular prisim A is 15 square inches and its altitude is 8 inches. Rectangular prism B has a square base that measures 2 inches on each side. If prisim A and prisim B have the same volumes, what must be the altitude of prisim b?
Volume of any regular right prism is base area*altitude*1/3
volume A= Volume B
1/3 15*8=1/3*2^2*H
solve for h.
Thank you!
To find the height or altitude of prism B, we need to compare the volumes of the two prisms. The formula for the volume of a triangular prism is V = (base area) x (altitude).
Given in the problem:
Base area of prism A (triangle) = 15 square inches
Altitude of prism A = 8 inches
Base area of prism B (square) = 2 inches x 2 inches
Let's calculate the volume of prism A first:
Volume of prism A = (base area of prism A) x (altitude of prism A)
= 15 square inches x 8 inches
= 120 cubic inches
Since both prisms have the same volume, we can equate the volumes:
Volume of prism A = Volume of prism B
Using the formula for the volume of a rectangular prism, which is V = (length) x (width) x (height), we can express the volume of prism B:
Volume of prism B = (base area of prism B) x (altitude of prism B)
= (2 inches x 2 inches) x (altitude of prism B)
= 4 square inches x (altitude of prism B)
Now, let's set up an equation by equating the volumes of prism A and prism B:
120 cubic inches = 4 square inches x (altitude of prism B)
To solve for the altitude of prism B, divide both sides of the equation by 4 square inches:
120 cubic inches / 4 square inches = altitude of prism B
The square inches on the right side of the equation cancel out, leaving us with:
30 inches = altitude of prism B
Therefore, the altitude of prism B must be 30 inches.