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Snacks at the Art Walk are sold in containers shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing. 8.7A) Which statement about the volumes of the cylinder and cone is true? 2 The volume of the cylinder is about 6.28 cubic inches less than the volume of the cone. The volume of the cylinder is about 6.28 cubic Inches greater than the volume of the cone. The volume of a cone is about 6.28 cubic inches oreater than the volume of the D. The volume of the cone is congruent to the volume of the cone.

User Vlad Sankin
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1 Answer

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Volumes

In order to compare both volumes we want to find the volume of each figure:

Volume of the cylinder

In order to find its volume we first find the area of its base.

Since its base is a circle, its area is given by

base area = π · r²,

where π and r are numbers:

π is pi and r is the radius of the base.

Since

π = 3.14

and

r = 2 in,

then

base area = 3.14 · (2 in)²

= 3.14 · 4 in²

= 12.56 in²

The volume is the product of the base area by the height of the cylinder:

volume cylinder = base area · height

volume cylinder = π · r² · h

= 12.56 in² · 8 in

= 100.48 in³

Then, the volume of the cylinder is 100.48 in³.

Volume of the cone

As we did before, in order to find its volume we first find the area of its base.

We use the equation

base area = π · r²,

where

π = 3.14

and

r = 3 in.

Then

base area = 3.14 · (3 in)²

base area = 28.26 in²

We multiply the base area by 1/3 the height (10 in) of the cone

cone volume = 1/3 · base area · height

cone volume = 1/3 · π · r² · h

= 1/3 · 28.26 in² · 10 in

= 94.2 in³

Then, the volume of the cone is 94.2 in³.

Comparison

Since the volume of the cylinder is 100.48 in³ and the volume of the cone is 94.2 in³. We observe that the volume of the cylinder is bigger (it takes up more space than the cone).

Since

100.48 in³ - 94.20 in³ = 6.28 in³

Then the volume of the cylinder is 6.28 in³ greater than the cone's volume.

Answer: B

Snacks at the Art Walk are sold in containers shaped like a cone or a cylinder. The-example-1
Snacks at the Art Walk are sold in containers shaped like a cone or a cylinder. The-example-2
User Naresh Pansuriya
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