For each pair of quantities given below, check whether the first is pr

1.	For each pair of quantities given below, check whether the first is proportional to the second. For proportional quantities, calculate the constant of proportionality.i. Perimeter and radius of circles.ii. Area and radius of circles.iii. The distance travelled and the number of rotations of a circular ring moving along a line.iv. The interest got in a year and the amount deposited in a scheme in which interest is compounded annually.v. The volume of water poured into a hollow prism and the height of the water level.
Answer» i. The perimeter of a circle is n times its diameter. That is 2n times the radius. ∴ Perimeter = 2πr ∴ The perimeter and radius are proportional. The constant of proportionality is 2π ii. The area of a circle is π times the square of the radius. ∴ Area = πr² ∴ Area and radius are not proportional. iii. When the ring rotates once, the distance travelled is equal to its perimeter. When it rotates twice the distance travelled is twice its perimeter. When it rotates ‘n’ times, the distance travelled is ‘n ‘ times the perimeter of the ring. iv. If the amount deposited is P and the rate of interest is R. Annual interest = I = PNR, I = P × R (N = 1) The amount and interest are proportional. Constant of proportionality is rate of interest, R. v. Volume of a hollow prism = base × height Volume, of water and height of water level, are proportional. Constant of proportionality is the base area.

For each pair of quantities given below, check whether the first is proportional to the second. For proportional quantities, calculate the constant of proportionality.i. Perimeter and radius of circles.ii. Area and radius of circles.iii. The distance travelled and the number of rotations of a circular ring moving along a line.iv. The interest got in a year and the amount deposited in a scheme in which interest is compounded annually.v. The volume of water poured into a hollow prism and the height of the water level.

Answer»

i. The perimeter of a circle is n times its diameter.

That is 2n times the radius.

∴ Perimeter = 2πr

∴ The perimeter and radius are proportional.

The constant of proportionality is 2π

ii. The area of a circle is π times the square of the radius.

∴ Area = πr²

∴ Area and radius are not proportional.

iii. When the ring rotates once, the distance travelled is equal to its perimeter. When it rotates twice the distance travelled is twice its perimeter. When it rotates ‘n’ times, the distance travelled is ‘n ‘ times the perimeter of the ring.

iv. If the amount deposited is P and the rate of interest is R.

Annual interest = I = PNR,

I = P × R (N = 1)

The amount and interest are proportional. Constant of proportionality is rate of interest, R.

v. Volume of a hollow prism = base × height

Volume, of water and height of water level, are proportional. Constant of proportionality is the base area.

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