Question

A semicircular sheet of metal of radius 14 cm is
bent to form an open conical cup.
Find the capacity of the cup.
Please help me. ​

Answer 1

Question :

A semicircular sheet of metal of radius 14 cm is bent to form an open conical cup. Find the capacity of the cup.

Solution :

Radius of semi - circular piece =14 cm

Circumference of semi - circle $=\pi r$

$= \frac{22}{7}\times14\\\\\\=44cm$

Circumference of base of cone = 44 cm

$2\pi r=44cm\\\\\\\to R=\frac{44\times7}{2\times22}\\\\\\=7cm$

Radius of semi - circular sheet = slant height of conical cup $\to 1=14cm$

Now,

$R^2+h^2\\\\\\=1^2\\\\\\\to 7^2+h^2=14^2\\\\\\\to h = \sqrt{196-49} \\\\\\=\sqrt{147} \\\\\\=7\sqrt{3} cm$

$\textsf{Capacity of cup =}\frac{1}{3}\pi R^2H\\\\\\=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 7\sqrt{3}\\\\\\=622.37cm^3$

Answer :

The Capacity of cup  = 622.37 cm³

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