Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

Answer:

Volume of a cone is 1/3 the volume of a cylinder with the same base.

Cone = V= 1/3 Bh where the B = the base area and h is the height

Area of a circle = πr² (if the diameter is 8 the radius of this circle is 4)

A = π4² = π16 usually notated as 16π (numerical coefficients come first)

V= 1/3 x 16 x 18

V= 6 x 16 (I took 1/3 of 18 which is 6)

V of the cone = 96 π in³

Volume of a cylinder is = Bh or in this case 16π x 18 = 288π

Comparing the two you can see that the cylinder is 3 x the volume of the cone or the cone is 1/3 the volume of the cylinder.

Answer 2

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$\bold { \underline{ \underline \orange{given}}} \orange→$

diameter of cylinder :- 8 inches

radius of cylinder :- 8/2 = 4 inches

height of cylinder :- 9 inches

diameter of cone :- 8 inches

radius of cone :- 8/2 = 4inches

height of cone :- 18 inches

π = 3.14

$\bold { \underline{ \underline \orange{solution}}} \orange→$

we know that

$\bold{volume \: of \: cylinder = \pi {r}^{2} h} \\ \\ \implies \: v1 = \pi \times {4}^{2} \times 9 \\ \\ \implies v1 = 16 \times 9 \times \pi \: \\ \\ \implies \: v1 = 144\pi \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: v1 = 144 \times 3.14 \\ \\ \implies \: v1 = 452.16 \: \: \: \: \: \: \: \:$

so volume of cylinder is 452.16 cube inch or 144π cubic inch

now we know that..

$\bold{volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h} \\ \\ \: \: \: \: \: \: \: \: \: \: \implies v2 = \frac{1}{3} \times \pi \times {4}^{2} \times 18 \\ \\ \implies \: v2 = 16 \times 6 \times \pi \: \\ \\ \implies \: v2 = 96\pi \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: v2 = 96 \times 3.14 \: \: \: \: \\ \\ \implies \: v2 = 301.44 \: \: \: \: \: \: \: \: \:$

so volume of cone is 301.44 cube inch or 96π cubic inch

now we get;

V1 = 452.16 cubic inch or 144π cubic inch

V2 = 301.44 cubic inch or 96π cubic inch

$v1 - v2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 452.16 - 301.44 \\ = 150.72 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

1) hence, volume of cylinder is 150.72 cubic inch more than volume of cone

$\frac{v1}{v2} = \frac{144\pi}{96\pi} = \frac{3}{2} \\ \: \: \: \:$

2) hence, ratio of Volume of cylinder and volume of cone is 3:2

that means, volume of this cylinder is 1.5 times greater than volume of this cone