Question

Which pyramid has a greater volume, and how much greater is its volume? A rectangular pyramid on the left with a base of 7 inches by 6 inches and height of 3 inches. A rectangular pyramid on the right with a base of 4 inches by 3 inches and a height of 10 inches.

Answer 1

A

Explanation:

Answer 2

Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of
`42in^3`

How much greater is its volume? its volume is
`2in^3` greater than the second (right) pyramid

Explanation:

Equation to find the volume of a pyramid:

`V=(A_bh)/(3)`

where
`A_b` is the area of the base, and
`h` is the height.

• First pyramid:

length:
`l=7in`

width:
`w=6in`

height:
`h=3in`

Area of the rectangular base:

`A_b=lw\\A_b=7in*6in\\A_b=42in^2`

Volume of the first pyramid:

`V_1=(A_bh)/(3)\\ \\V_1=(42in^2*3in)/(3) \\\\V_1=(126in^3)/(3) \\\\V_1=42in^3`

• Second pyramid:

length:
`l=4in`

width:
`w=3in`

height:
`h=10in`

Area of the rectangular base:

`A_b=lw\\A_b=4in*3in\\A_b=12in^2`

Volume of the second pyramid:

`V_2=(A_bh)/(3) \\\\V_2=(12in^2*10in)/(3)\\ \\V_2=(120in^3)/(3) \\\\V_2=40in^3`

Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of
`42in^3`

How much greater is its volume? its volume is
`2in^3` greater than the second (right) pyramid