Mathematics: The circumference of the base of a cylinder is 24π mm. a similar cylinder has a base with circumference of 60π mm. the lateral area of the larger cylinder is 210π mm2. what is the lateral area of the smaller cylinder? 17.1π mm2 33.6π mm2 60π mm2 84π mm2

i dont know im stuiped Step-by-step explanation:...

The circumference of the base of a cylinder is - id241523246, taylorsamodell3217

amazinga

02.06.2020

Step 1

Find the scale factor

we know that

If the two cylinders are similar

then

The ratio between the circumference of the larger cylinder to the circumference of the smaller cylinder is equal to the scale factor

$Scale\ Factor=\frac{60\pi}{24\pi}=2.5$

Step 2

Find the lateral area of the smaller cylinder

we know that

If the two cylinders are similar

then

The ratio between the lateral area of the larger cylinder to the lateral area of the smaller cylinder is equal to the scale factor squared

Let

x--------> the lateral area of the larger cylinder

y-------> the lateral area of the smaller cylinder

z--------> the scale factor

$z^{2} =\frac{x}{y}$

In this problem we have

z=2.5

$x=210\pi\ mm^{2}$

substitute in the formula and solve for y

$2.5^{2} =\frac{210\pi}{y}$

$y=\frac{210\pi}{2.5^{2}}=33.6\pi\ mm^{2}$

therefore

the answer is

$33.6\pi\ mm^{2}$

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