Question

The surface area (in \(m^2\)) of a sphere of radius 7 cm is :(Use \(\pi= \frac{22}{7}\))

• A. 0.0616
• B. 6.16
• C. 61.6
• D. 0.616

Answer 1

The Correct Option is A

The formula to calculate the surface area of a sphere is given by \(A = 4\pi r^2\), where \(A\) is the surface area and \(r\) is the radius of the sphere.

Given: \(r = 7 \text{ cm}\) and \(\pi = \frac{22}{7}\), we need to find the surface area in \(m^2\).

First, convert the radius from centimeters to meters: \(r = \frac{7}{100}\text{ m}\).

Substituting the values into the formula:

\(A = 4 \times \frac{22}{7} \times \left(\frac{7}{100}\right)^2\)

Simplify this expression:

\(A = 4 \times \frac{22}{7} \times \frac{49}{10000}\)

Cancel the common factor of \(7\) in the numerator and denominator:

\(A = \frac{4 \times 22 \times 7}{7 \times 10000}\)

Now, compute the multiplication and division:

\(A = \frac{88 \times 7}{10000} = \frac{616}{10000} = 0.0616 \text{ m}^2\)

Therefore, the correct surface area is \(0.0616 \text{ m}^2\), which matches the first option.