Question

Chiyo has a toolbox with the shape below. A rectangular prism with a length of 8 inches, width of 15 inches, and height of 6 inches. A triangular prism with a triangular base with base 8 inches and height 3 inches. The prism has a height of 15 inches. Which statements are true about the toolbox? Select two options. The shape can be broken into a rectangular prism and a triangular prism. The shape can be broken into a rectangular prism and a rectangular pyramid. The formula for the volume of this figure is V = B h + one-third B h. The volume of the toolbox is 840 inches cubed The volume of the toolbox is 900 inches cubed

Answer 1

Answer:

Option A and E.

Step-by-step explanation:

It is given that Chiyo has a toolbox with the shape of a rectangular prism with a length of 8 inches, width of 15 inches, and height of 6 inches. A triangular prism with a triangular base with base 8 inches and height 3 inches. The prism has a height of 15 inches.  

The shape can be broken into a rectangular prism and a triangular prism.

So, option A is correct.

Volume of rectangular prism $=l\times b\times h$

Where, l is length , b is width and h is height.

$V_1=8\times 15\times 6=720$

Volume of triangular prism $=Bh$

Where, B is base area and h is height.

Area of triangular base is

$B=\dfrac{1}{2}\times 8\times 3=12$

So, volume of triangular prism is

$V_2=12\times 15$

$V_2=180$

So, volume of tool box is

$V=V_1+V_2=720+180=900\text{ inches cubed}$

Therefore, the correct option is E.