Question

The volume of a sphere is 4,500π cubic yards. What is the radius of the sphere?

Answer 1

Answer:

• 15 yards

Step-by-step explanation:

In this question we have provided volume of sphere that is 4500π cubic yards . And we are asked to find the radius of the sphere .

We know that ,

$\qquad \: \frak{Volume_{(Sphere)} = \dfrac{4}{3}\pi r {}^{3} } \quad \bigstar$

Where ,

• r refers to radius of circle

Solution : -

As in the question it is given that volume of sphere is 4500π . So equation it with volume formula :

$\dashrightarrow \: \qquad \: \dfrac{4}{3} \pi r {}^{3} = 4500\pi$

Step 1 : Cancelling π as they are present on both sides :

$\dashrightarrow \: \qquad \: \dfrac{4}{3} \cancel{\pi }r {}^{3} = 4500 \cancel{\pi}$

We get ,

$\dashrightarrow \: \qquad \: \dfrac{4}{3} r {}^{3} = 4500$

Step 2 : Multiplying with 3/4 on both sides :

$\dashrightarrow \: \qquad \: \dfrac{ \cancel{4}}{ \cancel{ 3}} r {}^{ 3} \times \dfrac{ \cancel{3}}{ \cancel{4}} = \cancel{ 4500} \times \dfrac{3}{ \cancel{4} }$

On further calculations, We get :

$\dashrightarrow \: \qquad \: r {}^{3} = 1125 \times 3$

$\dashrightarrow \: \qquad \:r {}^{3} = 3375$

Step 3 : Applying cube root on both sides :

$\dashrightarrow \: \qquad \: \sqrt[3]{r {}^{3} } = \sqrt[3]{3375}$

We get :

$\dashrightarrow \: \qquad \: \purple{\underline{\boxed{\frak{r = 15 \: yards}}}}$

• Therefore , radius of sphere is 15 yards .

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Answer 2

Answer:

• 15

Step-by-step explanation:

In the question it is given that the volume of a sphere is 4,500π cubic yards. And we have to find the radius.

We know that,

• 4/3πr³ = Volume of a sphere

Now, Substituting the values in the fomulae :

⇒ 4/3πr³ = 4500π

Cancelling π from both sides :

⇒ 4/3r³ = 4500

⇒ 4r³ = 4500 × 3

⇒ 4r³ = 13500

⇒ r³ = 13500/4

⇒ r³ = 3375

Taking cube root on both sides we get :

⇒ r = 15

Therefore,

• The radius of the sphere is 15 yards