Afrench fry stand at the fair serves their fries in paper cones. the cones have a radius of 22 inches and a height of 66 inches. it is a challenge to fill the narrow cones with their long fries. they want to use new cones that have the same volume as their existing cones but a larger radius of 44 inches. what will the height of the new cones be?

The height of the new cones will be 16.5 inches.

Step-by-step explanation:

We know that,

The volume of a cone is,

Where, r is the radius of the cone,

h is the height of the cone,

In the original cone,

r = 22 inches,

h = 66 inches,

Thus, the volume would be,

Also, for the new cone,

r = 44 inches,

Let H be the height,

So, the volume of the new cone would be,

According to the question,

Hence, the height of the new cones will be 16.5 inches.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2