We are asked to find how much more canvas is used to make Tepee B than Tepee A.
Tepee
Diameter
Height
A
14
6
B
20
9
The lateral area of a cone is L=π r l, where r is the radius and l is the slant height of the cone. First, let's find the equation for l in terms of h and r by the Pythagorean Theorem.
l^2= r^2+ h^2
⇓
l=sqrt(r^2+ h^2)
Now, let's find the lateral area of the tepees.
Teppe
A
B
Height
h= 6
h= 9
Diameter
d=14
d=20
Radius
r=d/2
r=14/2= 7
r=20/2= 10
Slant Height
l=sqrt(r^2+ h^2)
l=sqrt(7^2+ 6^2)≈ 9.22
l=sqrt(10^2+ 9^2)≈ 13.45
Lateral Area
L=π r l
L=π( 7)( 9.22)≈ 202.76
L=π( 10)( 13.45)≈ 422.54
Therefore, the lateral area of Tepee B is about 422.54 square feet, and the lateral area of Tepee A is about 202.76 square feet. This tells us that about 422.54-202.76=219.78 square feet more canvas is used to make Tepee B than Tepee A.
