A semicircular sheet of metal whose diameter is 56 cm has been bent in

1.	A semicircular sheet of metal whose diameter is 56 cm has been bent in the shape of a conical bowl. What is the depth of the bowl?1. 14√62. 13√23. 12√34. 14√3
Answer» Correct Answer - Option 4 : 14√3 Given: The diameter of the semicircular sheet is 56 cm Concept Used: If a semicircular metal bent in the shape of a conical bowl then the slant height of the cone will be same as the radius of the semicircle. Calculation: The diameter of the semicircle is 56 cm The radius of the semicircle (r) = 28 cm That means the slant height of the cone (l) = 28 cm also The length of the semicircular sheet is πr ⇒ (22/7) × 28 ⇒ 88 cm That means the circumference of the base of the cone is also 88 cm Let the radius of the base of the cone is r₁ 2πr₁ = 88 ⇒ 2 × (22/7) × r₁ = 88 ⇒ r₁ = 14 The radius of the base of the conical bowl (r₁) = 14 cm Let, the height of the cone is h h = √(l² – r₁²) ⇒ h = √(28² – 14²) ⇒ h = √(784 – 196) ⇒ h = √588 ⇒ h = 14√3 ∴ The depth of the bowl is 14√3 cm.

A semicircular sheet of metal whose diameter is 56 cm has been bent in the shape of a conical bowl. What is the depth of the bowl?1. 14√62. 13√23. 12√34. 14√3

Answer» Correct Answer - Option 4 : 14√3

Given:

The diameter of the semicircular sheet is 56 cm

Concept Used:

If a semicircular metal bent in the shape of a conical bowl then the slant height of the cone will be same as the radius of the semicircle.

Calculation:

The diameter of the semicircle is 56 cm

The radius of the semicircle (r) = 28 cm

That means the slant height of the cone (l) = 28 cm also

The length of the semicircular sheet is πr

⇒ (22/7) × 28

⇒ 88 cm

That means the circumference of the base of the cone is also 88 cm

Let the radius of the base of the cone is r₁

2πr₁ = 88

⇒ 2 × (22/7) × r₁ = 88

⇒ r₁ = 14

The radius of the base of the conical bowl (r₁) = 14 cm

Let, the height of the cone is h

h = √(l² – r₁²)

⇒ h = √(28² – 14²)

⇒ h = √(784 – 196)

⇒ h = √588

⇒ h = 14√3

∴ The depth of the bowl is 14√3 cm.