SAT Math Example Problem – A Girl and Her Sandbox

Girl in her sandboxA girl is playing in a sandbox. She wants to decrease the volume of the sand in the sandbox by scooping sand and dumping it outside of the sandbox. The girls is a rather inquisitive mathematician and measures the dimensions of her sandbox. She finds the width and length to be 5 feet each and the height to be 4 feet. The sand in the sandbox goes all the way to the top. She wants to lower the volume of the sand to 50 cubic feet. How many feet of sand does she have to scoop out?

The first step in solving this problem is to find the volume of the sandbox when it’s full of sand. This is expressed like so:

V = lwh (Volume = length x width x height)

= 5(5)(4)

= 100 cubic feet

The volume of the sandbox full of sand is 100 cubic feet. The girl needs to lower the volume to 50 cubic feet of sand. Since she can’t change the width and length of the box, he has to change the height of the sand. This means the volume has to be set equal to 50 cubic feet, l and w have to remain constant, and the new height h of the sand must be solved for.

50 = 5(5)(h)

50 = 25h

2 = h

The new height of the sand must be 2 feet for the volume of the sand in the sandbox to be 50 cubic feet. Therefore, the girl has to scoop out 2 feet of sand to lower the volume of the sandbox to 50 cubic feet.

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