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GREYUIT [131]
3 years ago
13

For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

the cake is 10 inches. Each edge of the square-shaped base is 8 inches. Find the volume of Mary's cake. Round your answer to the nearest cubic inch.

Mathematics
1 answer:
mihalych1998 [28]3 years ago
4 0

Answer:

V=196in^3

Step-by-step explanation:

The volume of a pyramid is:

V=\frac{A_{b}h}{3}

where A_{b} is the area of the base and h is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

A_{b}=l^2

where l is the length of the side: l=8in, thus:

A_{b}=(8in)^2\\A_{b}=64in^2

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

hypotenuse^2=leg1^2+leg2^2

substituting our values, and indicating that leg 1 is height h:

(10in)^2=h^2+(4in)^2

100in^2=h^2+16in^2

and solving for the height:

h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in

and finally we calculate the volume using this height and the area of the base:

V=\frac{A_{b}h}{3}

V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3

rounding to the nearest cubic inch: V=196in^3

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