A rectangular prism with a height of 9 inches and a volume of 162 cubic inches, a triangular prism with the same height and volume.
a) State the area of the base of each b) If the height is "h" express the base of the triangle in terms of "h"?

Question

You hired to design packaging. The first is to be a rectangular prism with a height of 9 inches and a volume of 162 cubic inches. The second package is to be a triangular prism with the same height and volume.

a) State the area of the base of each of the packages. Explain your findings.
b) If the triangular base of the triangular prism has a height length of "h" inches, express the base of the triangle in terms of "h".

James Atkins · Accepted Answer

Area of the base of each prism is #18# sq.in and the base of triangular base is #36/h# in. long.

The volume of rectangular prism is #V_r= A_r* H_r# where #A_r# is base area (rectangle) of prism. The volume of triangular prism is #V_t= A_t* H_t# where #A_t# is base area (triangular) of prism. #V_r=V_t = 162# cubic inch ; #H_r = H_t=9 # inch. #:. A_r=A_t = 162/9 = 18 # sq.inch Area of the triangle is # A_t =1/2*b_t*h = 18 :. b_t = (2*18)/h = 36/h# Area of the base of each prism is #18# sq.in and the length of base of triangular base is #36/h# in. [Ans]

Carson Arnold · Answer

undefined a) The area of the base of a rectangular prism with a volume of 162 cubic inches and a height of 9 inches is 18 square inches.

b) If the height of the triangular prism is "h", then the base of the triangle can be expressed in terms of "h" using the formula for the volume of a triangular prism: $ V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{height} $. Therefore, the base of the triangle would be $ \frac{2 \times V}{h \times h} $.

A rectangular prism with a height of 9 inches and a volume of 162 cubic inches, a triangular prism with the same height and volume. a) State the area of the base of each b) If the height is "h" express the base of the triangle in terms of "h"?