Question

13. A rectangular metal plate has a length of 65 cm
and a width of 35 cm. It is melted down and recast
into circular discs of the same thickness. How
many complete discs can be formed if
(a) the radius of each disc is 3 cm?
(b) the radius of each disc is 10 cm?
14. Calculate the radius of a circle whose area is equal
to the sum of the areas of three circles of radil
2 cm, 3 cm and 4 cm respectively​

Answer 1

Answer:

13.A) 80 discs

13.B) 7 discs

Step-by-step explanation:

13.

Total area of the plate is (65×35) cm.sq.

area of a disc having radius 3 cm is π×9 cm.sq.

area of a disc having radius 10 cm is π×100 cm.sq.

for 13.A) number of discs (whose radius is 3cm) = {(65×35)/(π×9)} = 80.46=80.

for 13.B) number of discs (whose radius is 10 cm) = {(65×35)/(π×100)} = 7.24 =7

14.

Area of circles having radius 2cm, 3cm, 4cm are 4π cm.sq. , 9π cm.sq. , 16π cm.sq. respectively.

Now, let the required radius of new circle is x cm.

Area of the new circle is π×(x^2) cm.sq.

According to the problem,

π×(x^2) = 4π + 9π + 16π

x^2. = 29

x = √29 = 5.385

Hence, the radius of new circle will be 5.385 cm.