# Please answer me Q#35 page#104 from the following link https://tstuition.wikispaces.com/file/view/3+-+Mensuration.pdf many many thanks

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samhouston | Certified Educator

Think of this shape as two pyramids joined together.  Find the area of one of the pyramids and multiply by 2.

Volume of pyramid = area of base * height * 1/3

The base is a square with sides of 10 cm.  The area of the base is 100 square cm.

Use the pythagorean theorem to find the height.

a^2 + b^2 = c^2

a is half the length of one of the sides, a = 5

c is the length of one of the sides, c = 10

b is the height of the pyramid.  solve for b

5^2 + b^2 = 10^2

25 + b^2 = 100

b^2 = 75

b = sqrt(75)

b = 5 * sqrt(3)

Volume of the pyramid = area of base * height

V = 100 * 5 * sqrt(3)

V = 500 * sqrt(3)

This is the volume of one of the pyramids.  Multiply this by 2.

1000 * sqrt(3)

1732.05 cubic cm

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