SSC GD 2021 PYQ — Question 67

The correct answer is option 4 i.e. 9462 cm³

Given:

In a right-angled triangle, the right angle is contained between the sides with lengths of 14 cm and 48 cm. It is made to revolve around the longer side

Formula used:

In a triangle ABC right angled at B, Pythagoras theorem;

(Hypotenuse)² = (Base)² + (Perpendicular)²         ---- (1)

Volume of cone = (1/3) × πr²h          ---- (2)

Where, r = radius and h = height

Calculations:

Let ABC a right angled triangle at B, using equation (1), we get

AB = 14 and BC = 48

⇒ AC² = AB² + BC²

⇒ AC² = 14² + 48²

⇒ AC² = 2500

⇒ AC = 50

We know that BF is perpendicular to AC, such that

⇒ BF × AC = AB × BC

⇒ BF = (14 × 48)/50

⇒ BF = 13.44

Now when triangle ABC is revolved around AC, we get two cones ABD and BCD

⇒ Radius = 13.44 

Height = AF/CF

Using equation (2), we get

Volume of the solid formed = Volume of cone ABD + Volume of cone BCD

= π × (13.44 × 13.44 × AF)/3 + π × (13.44 × 13.44 × CF)/3

= [π × (13.44 × 13.44) × (AF + CF)]/3

= [22/7 × (13.44 × 13.44) × 50]/3 = 9461.7 = 9462 cm³