Answer:
1) 32
2) 8 yards
Step-by-step explanation:
1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:
[tex]LA=2225-25^2=1600[/tex]
The lateral surface area is 4 times the area of one the congruent triangles.
[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]
[tex]\implies 1600=50x[/tex]
[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]
[tex]32=x[/tex]
Therefore the height of the slant surface is 32 yards
2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.
We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:
[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]
[tex]151.58=50.24+12.56l[/tex]
[tex]101.34=12.56l[/tex]
[tex]\frac{101.34}{12.56}=l[/tex]
l=8.06
To the nearest whole number, the slant height is 8 yards
