Question

The figure is made up of a cone and a cylinder. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box.

Answer 1

Answer

38 m³

Explanation

To solve this we are going to find the volumes of the cylinder and the cone separately, and then we are going to add them.

Volume of the cylinder:

$V=\pi r^2h$

where

$V$ is the volume of the cylinder

$r$ is the radius

$h$ is the height

We can infer from the picture that the radius of the cylinder is 3 mm and its height is 2 mm, so let's replace the values

$V=(3.14) (2mm)^2(2mm)$

$V=(3.14)(4mm^2)(2mm)$

$V=25.12mm^3$

Volume of the cone:

$V=\pi r^2\frac{h}{3}$

where

$V$ is the volume of the cone

$r$ is the radius

$h$ is the height

We can infer from our picture that the radius of the cone is 4 mm and its height is 3 mm, so let's replace the values

$V=(3.14)(2mm)^2(\frac{3mm}{3} )$

$V=(3.14)(4mm^2)(1m)$

$V=12.56mm^3$

Volume of the figure = area of the cylinder + area of the cone

Volume of the figure = $25.12mm^3+12.56mm^3=37.68m^3$

rounded to nearest integer:

Volume of the figure = $38m^3$

Answer 2

To, the nearest whole number the approximate volume of this figure will be 63 cubic millimeters.

Given,

The radius of the base of cylinder and cone is 2 mm.

The height of the cylinder is 4 mm.

The height of cone is 3 mm.

We have to find the volume of the figure.

How to calculate the volume of the given shape?

Since the figure is combined of two shapes, a cone and a cylinder.

So we find the volume of each shape separately and add up to find the volume of the whole shape.

We know that volume of cylinder is,

$V=\pi r^{2} \times h$

$V=3.14\times 2^2\times 4$

$V=3.14\times 16$

$V=50.24 \ mm^3$

Now the volume of cone is,

$V'=\dfrac{1}{3} \pi r^{2} \times h$

$V'=\dfrac{1}{3} \times 3.14\times 2^2\times 3$

$V'= 4 \times 3.14$$V'=12.56\ mm^3$

The volume of the figure will be

$V+V'=50.24+12.56 \\V+V'=62.80\ mm^3$

So, the nearest whole number value to this volume is 63 cubic millimeters.

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