Question

Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 8 feet long, 5 feet wide, and 4 feet deep. She can purchase sand for the sandbox for $20 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)

(Round your answer to the nearest dollar.)

Answer 1

Explanation:

The wooden frame is a cuboid

and the volume of a cuboid = Length x Width x Depth

Therefore,

The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)

= 160 cubic feet

The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)

Unit conversion has to be applied then:

1 foot = 0.3048 meters

1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)

1 cubic feet =
`0.3048^(3)` cubic meters

Therefore: 160 cubic feet = (160)(
`0.3048^(3)`) cubic meters

Cost of sand:
1 cubic meter = $20

Therefore: (160)(
`0.3048^(3)`) cubic meters = $(20)(160)(
`0.3048^(3)`)

= $90.61

= $91 (Rounded to the nearest dollar)

It will cost Andrea $91 to purchase sand for the sandbox