Solving for Spherical Tank Volume

This solution explains how to calculate the volume of a spherical tank given its diameter. We will use the standard formula for the volume of a sphere and apply the given values step-by-step.

Understanding the Formula

The volume ($V$) of a sphere is calculated using the formula:

$ V = \frac{4}{3} \pi r^3 $

Where:

• $V$ is the volume of the sphere.
• $\pi$ (pi) is a mathematical constant, given as 3.141 in this problem.
• $r$ is the radius of the sphere.

Identifying Given Information

From the question, we have:

• Diameter of the spherical tank ($d$): 10 metres
• Value of pi ($\pi$): 3.141

Calculating the Radius

The radius ($r$) of a sphere is half of its diameter ($d$).

$ r = \frac{d}{2} $

Substituting the given diameter:

$ r = \frac{10 \text{ metres}}{2} $

$ r = 5 \text{ metres} $

Calculating the Volume

Now, we substitute the calculated radius and the given value of $\pi$ into the volume formula:

$ V = \frac{4}{3} \pi r^3 $

$ V = \frac{4}{3} \times 3.141 \times (5 \text{ metres})^3 $

First, calculate the cube of the radius:

$ (5 \text{ metres})^3 = 5 \times 5 \times 5 = 125 \text{ cubic metres} $

Now, substitute this back into the volume equation:

$ V = \frac{4}{3} \times 3.141 \times 125 \text{ m}^3 $

Multiply the numbers:

$ V = \frac{4 \times 3.141 \times 125}{3} \text{ m}^3 $

$ V = \frac{1570.5}{3} \text{ m}^3 $

Finally, perform the division:

$ V = 523.5 \text{ m}^3 $

Conclusion

The volume of the spherical tank is 523.5 cubic metres.