Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The volume of the largest sphere which can be carved out of a cube of side 6 cm is
(a)$113.14 \mathrm{cm}^{3}$
(b)$166 \mathrm{cm}^{3}$
(c)$179.66 \mathrm{cm}^{3}$
(d)$188.52 \mathrm{cm}^{3}$
Answer
Answer (as printed): A
Explanation
Clearly, the largest sphere that can be carved out of a cube will have a diameter equal to the edge of the cube. $$\text { So, radius of the sphere }=\frac{6}{2}=3 \mathrm{cm} \text {. }$$ ∴ Volume of the sphere $$=\left(\frac{4}{3} \times \frac{22}{7} \times 3^{3}\right) \mathrm{cm}^{3}=\frac{792}{7} \mathrm{cm}^{3}=113.14 \mathrm{cm}^{3} .$$