Question

7

.
Marisela wants to create a trophy in the shape of a rectangular
pyramid with volume 0.1875 cubic foot. Complete the descriptions
by writing in the missing measurements. 7.6.6
Design #1: pyramid height = 1.5 ft; base width = 0.75 ft;

Answer 1

Volume of a rectangular pyramid:

`V=\frac13lwh`

where:

• 
  `V` = volume
• 
  `l` = length of base
• 
  `w` = width of base
• 
  `h` = height

Given:

• 
  `V` = 0.1875 ft³
• 
  `w` = 0.75 ft
• 
  `h` = 1.5 ft

Substitute given values into the formula and solve for
`l`:

`\implies 0.1875=\frac13 \cdot l \cdot 0.75 \cdot 1.5`

`\implies 0.1875=(1.125)/(3) l`

`\implies 0.1875=0.375 l`

`\implies l=(0.1875)/(0.375)`

`\implies l=0.5`

Therefore, the base length is 0.5 ft