MCQ
A largest sphere of radius 3.5 cm is carved out from a cubical solid. The difference between their surface areas is
- A$224 cm^2$
- ✓$140 cm^2$
- C$176 cm^2$
- D$80.5 cm^2$
✓
Answer
Correct option: B.
$140 cm^2$
(B) $140 cm^2$
We have, $r=$ radius of the sphere $=3.5 cm$
$\therefore \quad a=\text { Length of an edge of the cubical solid }=2 r=7 cm$
Hence, required difference
$=6 a^2-\frac{4}{3} \pi r^3=6 \times 7^2-4 \times \frac{22}{7} \times\left(\frac{7}{2}\right)^2=(294-154) cm ^2 = 140 cm^2$
We have, $r=$ radius of the sphere $=3.5 cm$
$\therefore \quad a=\text { Length of an edge of the cubical solid }=2 r=7 cm$
Hence, required difference
$=6 a^2-\frac{4}{3} \pi r^3=6 \times 7^2-4 \times \frac{22}{7} \times\left(\frac{7}{2}\right)^2=(294-154) cm ^2 = 140 cm^2$
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