Find the volume of a sphere whose diameter is $ 6 ext{ cm}$.

Question

Find the volume of a sphere whose diameter is $ 6	ext{ cm}$.

Examoogle · Accepted Answer

The correct answer is Option B: $36\pi	ext{ cm}^3$. Calculate the radius as half the diameter ($r = 3$), then remember $3^3 = 27$. Dividing by 3 gives 9, and multiplying by the formula coefficient 4 yields $36\pi$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the radius as half the diameter ($r = 3$), then remember $3^3 = 27$. Dividing by 3 gives 9, and multiplying by the formula coefficient 4 yields $36\pi$.

Formula Used: $$V = \frac{4}{3} \pi r^3$$

Given: Diameter of the sphere d = 6 cm.

Steps: Determine the radius: Since the diameter of the sphere is given as $d = 6$ cm, the radius $r$ is half of the diameter.. Apply volume formula: The volume $V$ of a sphere is calculated using the formula $V = \frac{4}{3} \pi r^3$.. Final calculation: Substitute $r = 3$ into the equation: $V = \frac{4}{3} 	imes \pi 	imes 27$. Simplifying this gives $4 	imes \pi 	imes 9$.

Answer: B is correct because calculating the volume with a radius of 3 cm results in exactly 36π cm³.

Exam Tip: This is a standard 3D geometry problem; always convert diameter to radius first to avoid errors in all volume or surface area problems involving spheres or cylinders.

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