A conveyor belt dumps 2500 yd3 of gravel to form a cone-shaped pile. How high could this pile of gravel be, and what could the circumference of the pile of gravel be at ground level

Explanation:

Volume of the cone = 1/3πr²h

r is the radius

h is the height

2500 = 1/3πr²h

Criss multiply

r²h = 2500 × 3π

Rewrite the expression

r²h = 50² × 3π

Compare values

r² = 50²

r = √50²

r = 50yd

The radius is 50yards

Also;

h = 3π yards

h = 3(3.14)

h = 9.42yards

Hence the pile is 9.42yards high

Circumference of the pile = 2πr

Given r = 50

Substitute

Circumference = 2π(50)

Circumference = 100π

Circumference = 100(3.14)

Circumference = 314yards

Hence the circumference of the pile at the ground level is 314yards

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