Question

1. A semicircular instrument as shown in the following figure is made of a metal (shaded
region). If the cost of the metal is 10 per sq. cm, calculate the total cost of the metal
the model
used in the instrument.
7 cm
14 cm
Fig. 21.24​

Answer 1

Answer:

$577.5\: \: cm ^{2}$

Step-by-step explanation:

AREA OF SMALLER SEMI CIRCLE =>

$= > \frac{1}{2} \times \pi r ^{2}$

$= > \frac{1}{2} \times \pi \times {3.5}^{2}$

$= > \frac{1}{2} \times \frac{22}{7} \times 3.5 \times 3.5$

$= > \frac{11}{7} \times12.25$

$= > \frac{11}{7} \times \frac{1225}{100}$

$= > \frac{11 \times 175}{100}$

$= > \frac{1925}{100}$

$= > 19.25 \: \: cm ^{2}$

AREA OF BIGGER SEMI CIRCLE =>

$= > \frac{1}{2}\pi {r}^{2}$

$= > \frac{1}{2} \times \frac{22}{7} \times {7}^{2}$

$= > \frac{11}{7} \times 49$

$= > 77cm ^{2}$

• AREA OF BIGGER SEMI CIRCLE - AREA OF SMALLER SEMI CIRCLE = AREA OF SHADED REGION -:

$= > 77 - 19.25 \: cm^{2}$

$= > 57.75 \:cm ^{2}$

• TOTAL COST OF THE METAL USED IN THE INSTRUMENT =>

$= > 57 .75 \times 1 0$

$= > \frac{5775}{100} \times 10$

$= > 577.5 \: cm ^{2}$

HOPE THIS HELPS YOU☺️

AKRITI❤️