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In this lesson, we will learn about the volume of a sphere.

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Let's start, consider this sphere. Now, this sphere has the radius r.

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The formula to find the volume of this sphere, V is 4 over 3 pi r cube.

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Let's see some examples on how to use this formula. For these examples, we take pi as, 3.14

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First example, find the volume of this sphere when its radius is 4cm.

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Since the radius is given as 4 cm, we can substitute 'r' with 4.

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Now, let's simplify 4 cube. To do so, 4 cube is the same as 4 multiply by 4 multiply by 4, which is equals to 64.

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Let's write this down here.

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Next, since pi is given as 3.14. We can substitute this pi with 3.14.

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From here, we can find the volume by calculating these numbers.

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3.14 multiply by 64 gives 200.96.

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Now, this term is the same as 4 multiply by 200.96 over the 3.

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We can multiply 4 with 200.96. This gives 803.84.

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Next, 803.84 divide by 3 gives 267.95.

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Note that, this number has no meaning unless we include the unit for it.

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Since the radius is in centimeter, the volume will be in cubic centimeter.

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Hence, the volume of this sphere is 267.95 cubic centimeter.

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Next example, the volume of this sphere is 113.04 cubic ft. Find its radius, r.

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Now, let's begin with the formula for the volume of a sphere, V = 4 over 3 pi r cube.

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Here, we can see that since the volume and pi are given, we can find the radius, r, by solving this equation for r. Here’s how.

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First, it is easier to work with this equation if we rewrite it as, V equals 4 pi r cube, over 3.

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Next, note that we can remove the fraction in this equation, by multiplying both sides of the equation with 3.

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This gives, 3V equals to 4 pi r cube. Now, since pi is given as 3.14, we can substitute this pi with 3.14.

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Next, we multiply 4 with 3.14. This gives 12.56.

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Next, we can substitute V with 114.04.

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3 multiply with 113.04 gives, 339.12.

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Alright, now we have 12.56 r cube, equals to 339.12.

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Let's rewrite this equation so it will looks neater.

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Now, notice that, to get closer to find r, we need to remove 12.56.

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To do so, we divide both sides of the equation with 12.56.

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By doing so, we have r cube equals to, 339.12 over 12.56.

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Next, we divide 339.12 with 12.56. This gives 27.

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Now, since r cube is equals to 27, we can find r, by calculating the cube root of 27.

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Cube root of 27 gives 3.

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Again, this number has no meaning unless we include the unit for it.

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Since the volume is in cubic feet, the radius of the sphere will be in feet.

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Hence, the radius of the sphere is 3 ft.

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This is all for this lesson. Try out the practice question to further your understanding.

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