Question

Kaytlyn must build a sand castle in the form of a square pyramid for a project as shown to the left. She bought 3 bags of sand each containing 1200 inches cubed. Will she save enough sand to build the castle?

Answer 1

see the explanation

Explanation:

The complete question is

The dimensions of the square pyramid are

Base: 40 inches

Height: 12 inches

step 1

Find the volume of the square pyramid

The volume of the square Pyramid is given by the formula

`V=(1)/(3)b^2h`

where

b is the length side of the square base

h is the height of the pyramid

we have

`b=40\ in\\h=12\ in`

substitute

`V=(1)/(3)(40)^2(12)`

`V=6,400\ in^3`

step 2

Find the volume of sand

Multiply the number of bags of sand by the volume of each bag

so

`3(1,200)=3,600\ in^3`

step 3

Compare the volume of the sand with the volume of the square pyramid

3,600 < 6,400

therefore

Kaytlyn has not enough sand to build the castle