Mathematics: What is the volume of the item described? a rocket in the shape of a cylinder with radius 6 m and height 16 m with a cone on top of radius 6 m and height 3 m. select the exact answer in terms of π and the approximate answer rounded to the nearest whole number. 2149 m³ 612 π m³ 102 π m³ 320 m³ 1922 m³ 684 π m³

What is the volume of the item described? a rocket

harleymichaelbp74jsq

08.01.2022

Answer

612 π m³

1922 m³

Explanation

The body of the rocket is a cylinder; to find its volume, we are going to use the formula for the volume of a cylinder:

$V=\pi r^2h$

where

is the radius of the cylinder

is the height

We know from our problem that the radius of the cylinder is 6 m and its height is 16 m, so let's replace the values:

$V=\pi (6m)^2(16m)$

$V=\pi (36m^2)(16m)$

$V=576\pi m^3$

V=1809m^3

The volume of the cylinder is 1810m^3

To find the volume of the cone, we are going to use the formula:

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

where

is the radius

is the height

We know form our problem that the radius of the cone is 6 m and its height is 3 m, so let't replace the values:

$V=\pi (6m)^2(\frac{3m}{3} )$

$V=\pi (36m^2)(1m)$

$V=36\pi m^3$

V=113m^3

Now, we just need to add the volumes in terms of $\pi$ and the volumes rounded to the nearest whole:

Volume of the item in terms of π = $576\pi m^3+36\pi m^3=612\pi m^3$

Volume of the item rounded = 1809m^3+113m^3=1922m^3

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