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The volume formulas in mathematics are used to determine the total space occupied by any three-dimensional (3-D) object. Tennis balls, dice, and even our favorite ice cream cones are some of the examples of 3D objects. Now, let's go over the volume formulas for a few 3-D shapes in depth....Read MoreRead Less

The formula for volume is used to figure out how much space an object can hold or contain. The volume of any three-dimensional shape is measured in ‘units\(^3\)’ or cubic units. We have different 3-D objects in math such as cubes, cuboids, spheres, hemispheres, cones, cylinders, prisms, and pyramids.

So, before determining the volume of any three dimensional object, it is better to have a proper idea of its formula. The volume formula for each shape is clearly shown in the table below.

**Example 1:**

**Ron bought a brand-new toy ball with a radius of 4 inches for his brother Chris. Find the volume of this ball.**

**Solution:**

Given, the radius of the football, \(r=4\) inches.

As we know, the shape of a ball is a sphere.

So to find the volume of the ball, let’s use the formula to determine the volume of a sphere.

That is,

\(V=\frac{4}{3}\mathrm{\Pi}r^3\)

\(=\frac{4}{3}\times3.14\times{(4)}^3\)

\(=\frac{4}{3}\times3.14\times64\)

\(=\frac{4}{3}\times200.96\)

\(=\frac{803.84}{3}\)

\(=\) 267.94 inch\(^3\)

**Therefore, the volume of Chris’s toy ball is 267.94 cubic inches.**

**Example 2:****If the volume of a prism is 36 meter\(^3\) and the base area is 4 meter\(^2\), then, what would be the height of the prism?**

**Solution:**

As stated, the volume of a prism V = 36 meter\(^3\) and the base area is 4 meter\(^2\).

From the given data we can find the height of the prism using the formula:

V = area of base x height

36 = 4 x height

\(\frac{36}{4}\) = height

9 = height

**Hence, the height of the prism is 9 meters.**

**Example 3:****Camila wants to present her mother with a nice book. She found an empty cardboard box in the store room and thoughtfully decorated it to use as a gift box for the book. But Camila is unsure whether the book which has the volume of 180 units \(^3\) will fit in the box or not. Can Camila fit the book in the box that has the dimensions of \(10\times6\times5\)?**

**Solution:**

It is stated that the dimensions of the box are \(10\times6\times5\).

From this we can say that the box is in the shape of a cuboid.

So, the dimensions can be written as l = 10, b = 6, and h = 5.

We can find the quantity the box can contain by calculating its volume.

So, the formula for the volume of a cuboid is:

V = lbh

= \(10\times6\times5\)

= \(60\times5\)

= 300

**Therefore, the volume of the box is 300 units\(^3\).**

**Since, the volume of the book is 180 units\(^3\), Camila can use the box as a gift box for the book.**

Frequently Asked Questions

The relation between a prism and a pyramid is when a prism and pyramid have the same base and height, the volume of a pyramid is equal to 1/3 of the volume of the prism.

A sphere is a circular shaped ball that has a diameter or radius. However, a hemisphere is half of a sphere. Hence, the volume of a hemisphere will be half of the volume of the sphere.

The pyramids of Egypt, tents, cell phone towers, a piece of a watermelon and so on are some of the examples of pyramids.

Both prisms and pyramids are three dimensional objects that have flat-faces and bases. However, a pyramid has only one polygonal base, but a prism has two identical bases.

The volume of a cone equals one-third the volume of a cylinder that has the same radius and height of the cone.