Question

A right triangle of hypotenuse 13 cm and one of its sides 12 cm is made to
revolve taking side 12 cm as its axis. Find the volume and curved surface
area of the solid so form

Answer 1

Given :

• Hypothenuse (H) = 13cm
• One Side (P) = 12cm
• It is revolved, taking 12cm as its Axis.

To Find :

• Volume and Curved Surface Area of the solid so form.

Solution :

✰ In this question, Hypotenuse and one side of a Right Triangle are 13cm and 12cm respectively. So firstly we will find the Third side or Radius of the solid so form by using Pythagoras theorem and then we will find the Curved Surface Area and volume of the solid so form.

⠀⠀

⠀⠀⠀⟼⠀⠀⠀ (H)² = (P)² + (B)²

⠀⠀⠀⟼⠀⠀⠀ (13)² = (12)² + (B)²

⠀⠀⠀⟼⠀⠀⠀ 169 = 144 + (B)²

⠀⠀⠀⟼⠀⠀⠀ 169 - 144 = (B)²

⠀⠀⠀⟼⠀⠀⠀ 25 = (B)²

⠀⠀⠀⟼⠀⠀⠀ √25 = B

⠀⠀⠀⟼⠀⠀⠀ 5cm = B

⠀

Now, given Triangle is revolved, taking 12cm as its Axis.

➟ Radius of the Cone (r) = 5cm

➟ Height of the Cone (h) = 12cm

➟ Slant Height of the Cone (l) = 13cm

⠀

⠀⟹⠀⠀Curved Surface Area = πrl

⠀⟹⠀⠀Curved Surface Area = π(5)(13)

⠀⟹⠀⠀Curved Surface Area = 65πcm²

⠀

⟹⠀⠀Volume of Cone = ⅓πr²h

⟹⠀⠀Volume of Cone = ⅓π × 5 × 5 × 12

⟹⠀⠀Volume of Cone = ⅓π × 25 × 12

⟹⠀⠀Volume of Cone = ⅓π × 300

⟹⠀⠀Volume of Cone = 100πcm³

⠀

Hence, the volume and curved surface area of the solid so formed are 100πcm³ and 65πcm² respectively.

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