Question

a semicircular sheet of metal of diameter 28cm is bent into an open conical cup.find the depth and capacity of cup.(root 3=1.73)​

Answer 1

Step-by-step explanation:

semicircular sheet of paper of diameter 28 cm is bent into ... conical cup. find the depth and the capacity of the cup ... Height or depth of the conical cup = 12.124 cm

Answer 2

The depth of the cup is 12.11 cm.

The capacity of cup is 621.64 cm³.

Step-by-step explanation:

Given : A semicircular sheet of metal of diameter 28 cm is bent into an open conical cup.

To find : The depth and capacity of cup ?

Solution :

Diameter of the circular sheet is 28 cm.

Radius of the circular sheet is 14 cm.

Circumference of the semicircular sheet is $14\pi$.

A semicircular sheet of metal is bent into an open conical cup.

i.e. Slant height of conical cup = l=radius of circular sheet = 14 cm

Now,

Circumference of the base of the conical cup = Circumference of semicircular sheet

$2\pi R=14\pi$

$R=7\ cm$

Depth of conical cup = Height of the cone

i.e. $h=\sqrt{l^2-R^2}$

$h=\sqrt{(14)^2-(7)^2}$

$h=\sqrt{196-49}$

$h=\sqrt{147}$

$h=7\sqrt{3}$

$h=7\times 1.73=12.11\ cm$

The depth of the cup is 12.11 cm.

The capacity of the cup is $V=\frac{1}{3}\pi r^2 h$

$V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 12.11$

$V=621.64\ cm^3$

The capacity of cup is 621.64 cm³.

#Learn more

A semicircular sheet of metal of diameter 35cm is bent into an open conical cup find the depth and capacity of the cup

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