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Sliva [168]
3 years ago
12

A cylinder, cone, and sphere are shown below. The three figures have the same radius. The cylinder and cone have the same height

with h = r. If the volume of the cone is 36 cubic units, what are the volumes of the cylinder and the sphere? Explain how you found your answers. Answer in complete sentences and include all relevant calculations.

Mathematics
2 answers:
Pavlova-9 [17]3 years ago
7 0
<h2>Answer:</h2>

In this problem, we have three solids, namely:

1. A cylinder.

2. Cone.

3. sphere.

These three figures have the same radius. The cylinder and cone have the same height with h=r. We also know that:

Volume \ of \ the \ cone \ is \ 36units^3

Also, some formulas are provided:

Volume \ of \ a \ cylinder: V=\pi r^2h \\ \\ Volume \ of \ a \ cone: V=\frac{1}{3}\pi r^2h \\ \\ Volume \ of \ a \ sphere: V=\frac{4}{3}\pi r^3

Since h=r then our new formulas are:

Volume \ of \ a \ cylinder: V=\pi r^3 \\ \\ Volume \ of \ a \ cone: V=\frac{1}{3}\pi r^3 \\ \\ Volume \ of \ a \ sphere: V=\frac{4}{3}\pi r^3

For the cone, we know that V=36units^3 then we can get the radius r:

V=\frac{1}{3}\pi r^3 \\ \\ 36=\frac{1}{3}\pi r^3 \\ \\ 36(3)=\pi r^3 \\ \\ r^3=\frac{108}{\pi}

VOLUME OF THE CYLINDER:

V=\pi r^3 \\ \\ V=\pi \left(\frac{108}{\pi}\right) \\ \\ \boxed{V=108units^3}

VOLUME OF THE SPHERE:

V=\frac{4}{3}\pi r^3 \\ \\ V=\frac{4}{3}\pi \left(\frac{108}{\pi}\right) \\ \\ \boxed{V= 144units^3}

Solnce55 [7]3 years ago
5 0

Answer:

Vcylinder=107.8

Vsphere=143.79

Step-by-step explanation:

The first thing you should do is find the radius using the volume of the cone

Vcone=(1/3)pi h r^2

h=r

solving for r

\sqrt[3]{(\frac{3Vcone}{\pi } )} =r\\

r=[tex]\sqrt[3]{3*36/\pi } =r=3.25

Sphere=

V=(4/3)*pi*r^3

V=(4/3)*pi*(3.25)^3=143.79

cilinder

h=r

V=pi*r^3

V=pi*(3.25)^3=107.8

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