Question

. A semicircular sheet of metal of diameter 28cm is bent into an open conical cup. Find the depth
and capacity of cup.​

Answer 1

Diameter of the circular sheet is 28 cm.

Radius =14 cm

Circumference of semicircular sheet =14π cm

Now the semicircular sheet is bent into an open circular cup.

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

Circumference of the base of conical cup = Circumference of semicircle sheet = πr=14π (∵R=7 cm)

Depth of conical cup = Height of cone

$h = \sqrt{ {l}^{2} - {r }^{2} }$

$\sqrt{ {14 }^{2} { - 7}^{2} }$

$\sqrt{196 - 49}$

$\sqrt{147}$

$7 \sqrt{3}$

$capacity \: of \: the \: conical \: cup = \frac{1}{3} \pi {r}^{2}$

$\frac{1}{3} \times \frac{22}{7 \times} \times {7}^{2} \times 7 \sqrt{3}$

$\frac{1078 \sqrt{3} }{3} {cm}^{3}$