Topics
Total surface area of a sphere is \( \Large 154 cm^{2} \). Find its volume.
|
A) \( \Large 179.67\ cm^{3} \) |
|
B) \( \Large 169.33\ cm^{3} \) |
|
C) \( \Large 198.33\ cm^{3} \) |
|
D) \( \Large 186.67\ cm^{3} \) |
Correct Answer:
| A) \( \Large 179.67\ cm^{3} \) |
Description for Correct answer:
\( \Large r^{2} = 154 \times \frac{1}{4 \pi } \)
=\( \Large 154 \times \frac{7}{22} \times \frac{1}{4}=\frac{49}{4} \)
\( \Large r = \sqrt{\frac{49}{4}} = \frac{7}{2}\ cm. \)
Volume = \( \Large \frac{4}{3} \pi r^{3} \)
=\( \Large \frac{4}{3} \times \pi \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} \)
=\( \Large \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} \)
=\( \Large \frac{2 \times 11 \times 49}{6} = \frac{11 \times 49}{3} \)
= \( \Large \frac{539}{3} = 179.67\ cm^{3} \)
\( \Large r^{2} = 154 \times \frac{1}{4 \pi } \)
=\( \Large 154 \times \frac{7}{22} \times \frac{1}{4}=\frac{49}{4} \)
\( \Large r = \sqrt{\frac{49}{4}} = \frac{7}{2}\ cm. \)
Volume = \( \Large \frac{4}{3} \pi r^{3} \)
=\( \Large \frac{4}{3} \times \pi \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} \)
=\( \Large \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} \)
=\( \Large \frac{2 \times 11 \times 49}{6} = \frac{11 \times 49}{3} \)
= \( \Large \frac{539}{3} = 179.67\ cm^{3} \)
Part of solved Mensuration questions and answers : >> Aptitude >> Mensuration
Comments
Similar Questions
