A cone with the base radius have same base area as that of cylinder with same radius. The height of the specified cone is bigger than the height of the given cylinder.
What is the volume of a cone and a cylinder?
Suppose that the base of both the cone and the cylinder be r units and height h units.
Then,
The area of their bases will be B = [tex]\pi r^2[/tex]
[tex]\rm \text{Volume of cone} = \dfrac{1}{3} \pi r^2h = \dfrac{Bh}{3} \: \: \rm unit^3\\\\\text{Volume of cylinder} = \pi r^2h = Bh \: \: \rm unit^3[/tex]
It is given that both the cone and the cylinder have same base area
B = 78.5 sq. feet
Their volumes are given as:
Volume of cone = 314 cubic feet
Volume of cylinder = 785 cubic feet
Let we have height of cone as [tex]h_1[/tex] units.
Then,
[tex]\rm V_{cone} = B \times h_1 /3 = 78.5 \times h_1/3 \\314= 78.5 \times h_1/3 \\\\h_1 = \dfrac{314 \times 3}{78.5} = 12\: units\\[/tex]
Let the height of the cylinder be [tex]h_2[/tex] units, then
[tex]\rm V_{cylinder} = Bh = 78.5 \times h_2\\\\785 = 78.5 \times h_2\\\\\h_2 = \dfrac{785}{78.5} = 10 \: \rm units[/tex]
Thus, we see that height of the cylinder is smaller than the height of the cone in the given context.
Thus,
The height of the cone is bigger than the height of the cylinder.
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