Question

A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 800 cubic centimeters. Which equation can be used to find the area of the circular base?

Answer 1

For this case we can model the problem as a cylinder.
 The volume of a cylinder is given by:
 $V = Ab * h$
 Where,
 Ab: base area
 h: cylinder height
 Substituting values in the equation we have:
 $800 = Ab * 46$
 From here, we can clear the area of the base
 Answer:
 An equation that can be used to find the area of the circular base is:
 $800 = Ab * 46$

Answer 2

Answer:

The equation for the volume and area of a cylinder is best for modeling this case

V=πr²h

A=2πr

Step-by-step explanation:

Given

H= The height of the volcano 46cm

V= volume of volcano 800cm³

Volume of a cylinder is given as

V=πr²h

Substituting we have

800=3.142*r²*46

800=144.532r²

800/144.532=r²

r²=5.54

r= √5.54

r=2.35cm

We can use this radius to solve for the area

Area of circular base is given as

A=2πr

Substituting we have

A=2*3.142*2.35

A=14.78cm²