Question

The surface area of a sphere of diameter $\dfrac{1}{2}$ cm will be

• A. $\dfrac{\pi}{2}$ cm$^2$
• B. $\dfrac{\pi}{4}$ cm$^2$
• C. $\dfrac{\pi}{3}$ cm$^2$
• D. $\pi$ cm$^2$

Hint:

Always remember, Surface Area of a Sphere = $4\pi r^2$ and Volume = $\dfrac{4}{3}\pi r^3$.

Answer 1

The Correct Option is B

Step 1: Formula for surface area of a sphere.
\[ \text{Surface Area} = 4\pi r^2 \] Step 2: Find the radius.
Given diameter = $\dfrac{1}{2}$ cm \[ r = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4} \text{ cm} \] Step 3: Substitute in the formula.
\[ \text{Surface Area} = 4\pi \left(\dfrac{1}{4}\right)^2 = 4\pi \times \dfrac{1}{16} = \dfrac{\pi}{4} \text{ cm}^2 \] Step 4: Conclusion.
Therefore, the surface area of the sphere is $\dfrac{\pi}{4}$ cm$^2$.