Question

If the radius of a sphere is 3.5 cm, then the volume and total surface area of a sphere are respectively.... (use \(\pi=\frac{22}{7}\))

• A. \(\frac{539}{6} \text{ cm}^3 \quad \text{and} \quad 77 \text{ cm}^2\)
• B. \(\frac{539}{6} \text{ cm}^3 \quad \text{and} \quad \frac{147}{2} \text{ cm}^2\)
• C. \(\frac{539}{3} \text{ cm}^3 \quad \text{and} \quad 49 \text{ cm}^2\)
• D. \(\frac{539}{3} \text{ cm}^3 \quad \text{and} \quad 154 \text{ cm}^2\)

Answer 1

The Correct Option is D

To solve the problem, we need to calculate the volume and total surface area of a sphere with radius \( r = 3.5 \, \text{cm} \), using \( \pi = \frac{22}{7} \).

1. Formula for Volume of a Sphere:

The volume of a sphere is given by:

\( V = \frac{4}{3} \pi r^3 \)

2. Substituting the Values:

\( r = 3.5 = \frac{7}{2} \)

\( V = \frac{4}{3} \times \frac{22}{7} \times \left( \frac{7}{2} \right)^3 \)

\( = \frac{4}{3} \times \frac{22}{7} \times \frac{343}{8} \)

3. Simplifying the Volume:

\( V = \frac{4 \times 22 \times 343}{3 \times 7 \times 8} \)

\( = \frac{30184}{168} = \frac{539}{3} \, \text{cm}^3 \)

4. Formula for Surface Area of a Sphere:

Surface Area \( A = 4 \pi r^2 \)

5. Substituting the Values:

\( A = 4 \times \frac{22}{7} \times \left( \frac{7}{2} \right)^2 \)

\( = 4 \times \frac{22}{7} \times \frac{49}{4} \)

\( = \frac{22 \times 49}{7} = 154 \, \text{cm}^2 \)

Final Answer:

The volume is \( \frac{539}{3} \, \text{cm}^3 \) and the surface area is \( 154 \, \text{cm}^2 \).