Mathematics, 09.02.2021 14:00 uchechukwueigwe

When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm/min. At what rate is the plate's area increasing when the radius is 50 cm?

When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm/min.

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The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.Mar 13, 2020

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When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm/sec. At what rate is the plate's area increasing when the radius is 50 ...

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Oct 2, 2015 — At what rate is the plate's area increasing when the radius is 53 cm? I have to answer ... The rate of change of the area is [] cm^2/min. Follow • 2.

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MyMathLab: When a circular plate of metal is heated in an oven, its radius increases at a rate f 0.03 cm/min. At what rate is the plate's area increasing when the ...

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When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm/sec. At what rate is the plate's area increasing when the radius is 50 cm?

Answer · 24 votes

$\pi$ cm$^2$/sec

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When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min.

Answer · 0 votes

Let r = radius (in cm) at time t min A = area (in cm2) at time t min A = πr2 GIVEN: dr/dt = 0.02 cm/min FIND: dA/dt when r = 53 cm Differentiate the area formula with respect to t: dA/dt = π(2r)(dr/dt) = π(2(53 cm))(0.02 cm/min) = 2.12π cm2/min ≈ 6.66 cm2/min

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When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm divided by min. At what rate is the plate's area increasing when the radius is 43 cm?

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The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.Step-by-step explanation:The area of a circle is given by the following formula: $A = \pi r^{2}$ In which the area is measured in cm².Its radius increases at a rate of 0.04 cm divided by min.This means that $\frac{dr}{dt} = 0.04$ At what rate is the plate's area increasing when the radius is 43 cm?This is $\frac{dA}{dt}$ when r = 43 $A = \pi r^{2}$ Applying implicit differentitationWe have two variables(A and r), so $\frac{dA}{dt} = 2r\pi \frac{dr}{dt}$ $\frac{dA}{dt} = 2*43\pi*0.04$ $\frac{dA}{dt} = 10.81$ The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

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When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm divided by min0.02 cm/min. at what rate is the plate's area increasing when the radius is 4040 cm?

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Since the plate is circular, therefore the area of the plate is jut equal to the area of a circle, so: Area of plate = πr² = A Taking the derivative: dA / dr = 2πr ---> 1 By the idea of partial differentiation, the equation can also take in the form of:dA/dt = dA/dr x dr/dt ---> 2 Where we are given that:change in radius over time = dr/dt = 0.02 cm/minchange in area with changing radius = dA/dr = 2πr ---> from equation 1 at r = 40 dA/dr = 2π(40) = 80π Substituting all the known values into equation 2: dA/dt = (80π)(0.02) dA/dt = 1.6π cm^2 /s = 5.03 cm^2/s

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When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min. At what rate is the plate's area increasing when the radius is 60 cm? The rate of change of the area is□cm2/min. (Type an exact answer in terms of π.)

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here , for the radius , dr/dt = 0.02 cm/min r = 60 cm for the area rate of increase in area = dA/dt rate of increase in area = d/dt(pi * r^2) rate of increase in area = 2pi * r * dr/dt rate of increase in area = 2pi * 60 * 0.02 rate of increase in area = 7.54 cm^2/min the rate of increase in area is 7.54 cm2/min

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A circular metal plate expands under heating so that its radius increases by 2%. Find the approximate increase in the area of the plate if the radius of the plate before heating is 10 cm.

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