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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

Verified Answer :

cerverusdante

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

\(r\) is the radius of the cylinder

\(h\) 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

\(r\) is the radius

\(h\) 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 = \(1809m^3+113m^3=1922m^3\)

TropfJakob

Answer:

612 and 1922

Step-by-step explanation:

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