A ball of moulding clay, whose radius is a, is remoulded into a cube. What is the approximate length of the side of the largest cube that can be so made?

Correct option is C

Given:

• Radius of the sphere = $a$
• Volume of a sphere = $$V_{\text{sphere}} = \frac{4}{3} \pi r^3$$ 
• Side of the cube = $s$
• Volume of a cube = s³​

Formula Used:

Equate the volumes: $$\frac{4}{3} \pi a^3 = s^3$$

Solution:

Start by equating the volumes: $$\frac{4}{3} \pi a^3 = s^3$$​​

Solve for $s$: $$s = \left( \frac{4}{3} \pi a^3 \right)^{\frac{1}{3}}$$​​

​Approximate $\pi \approx 3.14$:$$s = \left( \frac{4}{3} \times 3.14 \times a^3 \right)^{\frac{1}{3}}$$​​

Simplify: $$s = \left( 4.1867 \times a^3 \right)^{\frac{1}{3}}$$​​

Take the cube root: s ≈ 1.6a

Final Answer:

The side length of the cube is approximately $1.6a$.

Correct Option: (c) 1.6a

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