The surface area of a sphere is 792/7 {cm}². Find, correct to the nearest whole number, its volume. [Take π = 22/7]

Correct Answer is : 113cm3{cm}³cm3

Correct Answer is : 113cm3{cm}³cm3

Test Index

WAEC Mathematics 2018 Paper

Question : 14

Total: 50

\frac{792}{7} \text{cm}^2

\pi = \frac{22}{7}

]

Solution:

Concept:

For a sphere, surface area is

4\pi r^2

and volume is

\frac{4}{3}\pi r^3

. First find the radius using the given surface area, then substitute it into the volume formula.

Explanation:

Given surface area

= \frac{792}{7} \text{ cm}^2

So,

4\pi r^2 = \frac{792}{7}

Using

\pi = \frac{22}{7}

4 \times \frac{22}{7} \times r^2 = \frac{792}{7}

Multiplying both sides by

\frac{7}{88}

gives

r^2 = 9

Therefore,

r = \sqrt{9} = 3 \text{ cm}

Now, volume of the sphere is

\frac{4}{3}\pi r^3

Substitute

r = 3

V = \frac{4}{3} \times \frac{22}{7} \times 3^3

V = \frac{4}{3} \times \frac{22}{7} \times 27 = \frac{792}{7} \approx 113.143

Correct to the nearest whole number,

V = 113 \text{ cm}^3

Answer:

113 \text{ cm}^3

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