Question

the diameter and volume of a right circular cone is 56 cm and 78848 cubic cm . find its slant height

Answer 1

Answer :

• Slant height is 100cm

Given :

• Diameter is 56cm
• Volume of right circular cone is 78848cm³
• Radius = 56/2 = 28cm

To find

• Slant height

Solution :

First of all , we have to find the height by using the formula of volume of cone

As we know that,

• Volume of cone = ⅓πr²h

⇢ 78848 = ⅓ × 22/7 × 28 × 28 × h

⇢ 78848 = ⅓ × 22 × 4 × 28 × h

⇢ 78848 × 3 = 22 × 4 × 28 × h

⇢ 236544 = 2464 × h

⇢ h = 236544/2464

⇢ h = 96cm

Hence , Height is 96cm

Now we have to find the slant height

As we know that ,

• Slant height = √r² + h²

Where , r is radius 28cm and h is height 96cm

⇢ √28² + 96² = l²

⇢ 784 + 9216 = l²

⇢ 10000 = l²

⇢ l = √10000

⇢ l = 100cm

Hence, Slant height is 100cm

More Explanation :

• Volume of cone = ⅓πr²h
• curved Surface area of cone = πrl
• Total surface area of cone = πrl + πr²