Question

A right circular cylinder and cone have equal bases and equal heights. If their CSA are in the ratio 8:5 show that the ratio between radius of their bases to their height is 3:4

Answer 1

Answer:

3 : 4

Step-by-step explanation:

Given A right circular cylinder and cone have equal bases and equal heights. If their CSA are in the ratio 8:5. We have to show that the ratio between radius of their bases to their height is 3:4.

Curved surface area of cylinder is 2πrh and curved surface area of cone is πrl.

They are in the ratio 8 : 5. It means

        2πrh /  πrl = 8 / 5 or h / l = 4 / 5

             h^2 / l^2 = 16 / 25 or l^2 = 25 / 16 h^2

    Now l^2 = h^2 + r^2

   25/16 h^2 = h^2 + r^2

  r^2 = 25/16 h^2 - h^2

r^2 = 9 / 16 h^2

or r / h = 3/4

or r : h = 3 : 4

Answer 2

HEY Buddy....!! here is ur answer

Let, the radius of base of the right circular cylinder and cone = r, and height = h

Then, Given that : Their CSA (Curved Surface Area) are in the ratio 8:5

As we know that : Curved Surface Area of a cone = πrl, and Curved Surface Area of a Cylinder = 2πrh

According to the question :

$\frac{2\pi \: rh}{\pi \: rl} = \frac{8}{5} \\ \\ = > \frac{h}{l} = \frac{4}{5} \\ \\ As \: we \: know \: that : \: {l}^{2} = {h}^{2} + {r}^{2} \\ \\ = > {5}^{2} - {4}^{2} = {r}^{2} \\ \\ = > {r}^{2} = 9 \\ \\ = > r = 3$

Now, the ratio of radius of their bases and their height will be :

r:h = 3:4 HENCE PROVED

I hope it will be helpful for you....!!

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