Question

A spherical tank holds 8,000 ft^3 of water. What is the diameter of the tank?

Answer 1

The diameter of the tank is 24.80 ft

Explanation:

Given-

• A spherical tank holds 8,000 ft^3 of water

i.e. The volume of spherical tank = 8,000 ft^3

Now, the formula for finding volume of any spherical figure is-

`\boxed{\mathfrak{ \purple{volume \:of \: sphere = (4)/(3) \pi {r}^(3) }}}`

Therefore, substituting value, we get

`⇢8000 = (4)/(3) \pi {r}^(3)`

`⇢8000 * (3)/(4 ) = (22)/(7) \pi {r}^(3)`

Transposing 4/3 to left hand side ,it will become 3/4 . And Here, 8000 will get cancelled by 4 leaving 2000

`⇢2000 * 3 * (7)/(22) = {r}^(3)`

Similarly , On performing further calculations, we get. ..

`⇢ (21000)/(11) = {r}^(3)`

`⇢1910.822 = {r}^(3)`

`⇢ \sqrt[3]{1910.822} = r`

`⇢ \underline{12.40 = r}`

Thus, the radius of the tank is 12.40 ft

Now,

The diameter of the tank = 2 × radius

`\: \: \: \: \: \: \: \: \: \: \: \: = 2 * 12.40`

`\: \: \: \: \: \: \: \: \: \: \: \: = 24.80`

•°• The diameter of the tank comes out 24.80 ft

Answer 2

24.8 ft

Explanation:

Formula to find the volume of a sphere is :

Volume =
`(4)/(3)` π r³

Here,

r ⇒ radius

Given that,

Volume ⇒ 8000 ft³

Let us find the radius of the tank now.

Volume =
`(4)/(3)` π r³

8000 =
`(4)/(3)` π r³

8000 =
`(4)/(3)` × 3.14 × r³

8000 × 3 = 4 × 3.14 × r³

24000 = 12.56r³

Divide both sides by 12.56.

1910.822 = r³

∛1910.822 = r

12.40 ft = radius

And now let us find the diameter of the sphere.

d = 2r

d = 2 × 12.40

d = 24.8 ft