What is the difference in the volume (in ) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm? Use $\pi =\frac{22}{7}$

The correct answer is 924 cm³ (Option 3).

We need to find the difference between the volume of a sphere with radius 7 cm and the volume of a cone with radius 7 cm and height 10 cm, using $\pi =\frac{22}{7}$.

Step 1: Calculate the Volume of the Sphere

The formula for the volume of a sphere of radius r is:

$V_{\text{sphere}}=\frac{4}{3}\pi r^3$

Substituting $r=7$ cm and $\pi =\frac{22}{7}$:

$V_{\text{sphere}}=\frac{4}{3}\times \frac{22}{7}\times 7^3$

Since $7^3=343$, and $\frac{343}{7}=49$:

$V_{\text{sphere}}=\frac{4}{3}\times 22\times 49=\frac{4312}{3}$ cm³

Step 2: Calculate the Volume of the Cone

The formula for the volume of a cone of radius r and height h is:

$V_{\text{cone}}=\frac{1}{3}\pi r^{2}h$

Substituting $r=7$ cm, $h=10$ cm, and $\pi =\frac{22}{7}$:

$V_{\text{cone}}=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 10$

Since $7^2=49$, and $\frac{49}{7}=7$:

$V_{\text{cone}}=\frac{1}{3}\times 22\times 7\times 10=\frac{1540}{3}$ cm³

Step 3: Find the Difference

Both volumes share the same denominator of 3, so we subtract directly:

$\text{Difference}=V_{\text{sphere}}-V_{\text{cone}}=\frac{4312}{3}-\frac{1540}{3}=\frac{2772}{3}$

$\text{Difference}=924$ cm³

Therefore, the difference in volume between the sphere and the cone is 924 cm³.