Question

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out.find the total surface area of the remaining solid.​

Answer 1

Given :-

• Diameter of cylinder = 1.4 cm
• Radius of cylinder = Diameter ÷ 2 = 1.4 ÷ 2 = 0.7 cm
• Radius of cone = 0.7 cm
• Height of cylinder = 2.4 cm
• Height of cone = 2.4 cm

To Find :-

• TSA of remaining solid = ?

Solution :-

Finding Slant Height of cone :

→ Slant Height = √(Height)² + (Radius)²

→ Slant Height = √(2.4)² + (0.7)²

→ Slant Height = √5.76 + 0.49

→ Slant Height = √6.25

→ Slant Height = 2.5 cm

Therefore, Slant Height of the cone is 2.5 cm.

Now, let's find the TSA of remaining solid :

Let radius of cylinder and cone be 'r' and height of cylinder and cone be 'h'

★ According to Question now :

⋙ TSA of remaining solid = CSA of cylinder + CSA of cone + base area of cylinder

⋙ TSA of remaining solid = 2πrh + πrl + πr²

⋙ TSA of remaining solid = πr(2h + l + r)

⋙ TSA of remaining solid = 22/7 × 0.7(2 × 2.4 + 2.5 + 0.7)

⋙ TSA of remaining solid = 22/7 × 7/10 (4.8 + 2.5 + 0.7)

⋙ TSA of remaining solid = 22/10(4.8 + 2.5 + 0.7)

⋙ TSA of remaining solid = 22/10× 8

⋙ TSA of remaining solid = 22/5 × 4

⋙ TSA of remaining solid = 88/5

⋙ TSA of remaining solid = 17.6 cm²

⋙ TSA of remaining solid = 18 cm² (approximately)

Therefore,TSA of remaining solid surface is 18 cm² (approximately).