From a solid right circular cylinder with height 10 cm and the radius of the bases 6 cm a right circular cone of the same height and the same base is removed. Find the volume of the remaining solid.
Answers
Answer:
Given, Radius of the base = 6 cm. It is given that a right circular cone of the same height and same base is removed. ⇒ 754.28 cm³ (or) 754.3 cm³. ⇒ Whole surface area = 710.6 cm².
Step-by-step explanation:
Given, Height of cylinder h = 10 cm.
Given, Radius of the base = 6 cm.
It is given that a right circular cone of the same height and same base is removed.
Required volume = Volume of cylinder - Volume of cone
⇒ πr²h - (1/3)πr²h
⇒ (22/7) * (6)² * 10 - (1/3) * (22/7) * (6)² * 10
⇒ (22/7)[360 - 120]
⇒ (22/7)[240]
⇒ 754.28 cm³ (or) 754.3 cm³.
Now,
We know that slant height (l) = √r^2 + h²
⇒ √6^2 + 10²
⇒ √136
⇒ 2√34
⇒ 11.66
Total surface area = (2πrh + πr² + πrl)
⇒ (2 * 22/7 * 6 * 10 + 22/7 * 6² + 22/7 * 6 * 11.66)
⇒ (22/7)[2 * 60 + 36 + 69.96]
⇒ (22/7)[225.96]
⇒ 710.6 cm²
Therefore:
⇒ Volume of the remaining solid = 754.28 (or) 754.3 cm³
⇒ Whole surface area = 710.6 cm².
Hope it helps!
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