Comprehension A student goes shopping by bicycle and travels the distance of 10 km to reach the shop in 50 minutes. He buys a cylinder whose volume of

Question

What is the slant height of a cone?
1. √(163) m
2. √(161) m
3. √(167) m
4. √(173) m
5. √(170) m

Answer 1

Correct Answer - Option 1 : √(163) m

Given:

The distance is travelled by him = 10 km

Reaching time = 50 minutes

⇒ (5/6) hours

The volume of a cylinder = 4620 m3

The volume of a cone = (1/7) × the volume of a cylinder

And the height of a cone = 10 m

Reduce time = (50 - 10)

⇒ 40 minutes

⇒ 40/60 hours

⇒ 2/3 hours 

Formula used:

Speed = (Distance/Time)

The volume of cylinder = πr2h

The curved surface area of a cylinder = 2πrh, where r is the radius of a cylinder and h is the height of a cylinder.

The volume of a cone = (1/3)πR2H, where R is the radius of a cone, H is the height of a cone and π is 22/7

The slant height of a cone = √(height2 + radius2)

Calculation:

The volume of a cone = (1/7) × 4620

⇒ 660 m³

The volume of a cone = (1/3)πR2 × 10

⇒ 660 = (10/3) × (22/7) × R2

⇒ R² = (660 × 3 × 7)/(10 × 22)   

⇒ R2 = 3 × 3 × 7

⇒ R = √(3 × 3 × 7)

⇒ R = 3√7 m

The slant height of cone = √[(10)2 + (3√7)²] 

⇒ √[100 + 63]  

⇒ √(163) m

∴ The slant height of a cone is √(163) m.