Question

1. If the surface area of a square pyramid is 2225 yards squared. The base of the pyramid has a length of 25 yards. What is the height of the slant on one of the lateral faces?

2. The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.

Answer 1

1) 32

2) 8 yards

Explanation:

1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:

`LA=2225-25^2=1600`

The lateral surface area is 4 times the area of one the congruent triangles.

`LA=4\cdot (1)/(2)\cdot 25\cdot x`

`\implies 1600=50x`

`\implies (1600)/(50)=(50x)/(50)`

`32=x`

Therefore the height of the slant surface is 32 yards

2) The surface area of a cone is
`S.A =\pi r^2+\pi r l`, where l is the slant height.

We substitute the surface area S.A=151.58 and
`\pi=3.14,r=4` to obtain:

`151.58=3.14\cdot 4^2+3.14\cdot 4 l`

`151.58=50.24+12.56l`

`101.34=12.56l`

`(101.34)/(12.56)=l`

l=8.06

To the nearest whole number, the slant height is 8 yards