If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in cm2/hour) is

Question

If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in cm2/hour) is (A) 5 π (B) 10 π (C) 100 π (D) 50 π

Tardigrade Admin · Accepted Answer

Let A = π r2 be area of metalic circular plate of r=50 cm. Also, given (dr/dt) = 1mm = (1/10)cm ∴ A = π r2 ⇒ (dA/dt) = 2π r(dr/dt) = 2π.50. (1/10) = 10π Hence, area of plate increases in 10π cm2/hour.

Q. If a metallic circular plate of radius $50 c m$ is heated so that its radius increases at the rate of $1 mm$ per hour, then the rate at which, the area of the plate increases (in $c m^{2}$ /hour) is

$5 π$

$10 π$

$100 π$

$50 π$

Let $A = π r^{2}$ be area of metalic circular plate of $r = 50 c m .$
Also, given $\frac{d r}{d t} = 1 mm = \frac{1}{10} c m$
$∴ A = π r^{2}$
$\Rightarrow \frac{d A}{d t} = 2 π r \frac{d r}{d t} = 2 π .50. \frac{1}{10} = 10 π$
Hence, area of plate increases in $10 π c m^{2} /$ hour.

Q. If a metallic circular plate of radius 50cm is heated so that its radius increases at the rate of 1mm per hour, then the rate at which, the area of the plate increases (in cm2/hour) is

5π

10π

100π

50π