Question

A semicircular sheet of tin is formed into a cone Show that the volume of the cone so formed is given by √3πR³/24 where R is the radius of semi- circle.

Answer 1

Given :- A semicircular sheet of tin is formed into a cone Show that the volume of the cone so formed is given by √3πR³/24 where R is the radius of semi- circle. ?

Solution :-

we know that, when a semicircular sheet is formed into cone ,

• Radius of semi - circle = slant height of cone .
• circumference of semi - circle = Base of cone .
• slant height = √[(radius)² + (height)²] .

so,

→ slant height of cone = Radius of semi - circle = R

and, Let us assume that, radius of cone is r and height is h .

→ Base of cone = π * R

→ 2 * π * r = π * R

→ 2r = R

→ r = (R/2)

then,

→ R = √[h² + (R/2)²]

→ R² = h² + (R²/4)

→ h² = R² - (R²/4)

→ h² = (3R²/4)

→ h = √3R/2

therefore,

→ Volume of cone = (1/3) * π * (r)² * h = (1/3) * π * (R/2)² * (√3R/2) = (1/3) * π * (R²/4) * (√3R/2) = (√3πR³/24) (Proved).

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Answer 2

Step-by-step explanation:

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