Question

(a = 22/
The ratio between the curved surface area and the total surface area of a right circular cylinder is
1: 1.Find the ratio between the height and radius of the cylinder.
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Answer 1

Given :-

• The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 1.

To Find :-

• The ratio between the height and radius of the cylinder.

Formula Used :-

${{ \boxed{\small{\bold\green{Curved \: Surface \: Area_{(Cylinder)}\: = \:2\pi r h }}}}}$

${{ \boxed{\small{\bold\red{Total \: Surface \: Area_{(Cylinder)}\: = \:2\pi r (h + r)}}}}}$

where,

• h = height of cylinder
• r = radius of cylinder

Solution :-

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 1.

$\bf\implies \:\dfrac{Curved \: Surface \: Area}{Total \: Surface \: Area} = \dfrac{1}{1}$

$\bf\implies \:\dfrac{2\pi \: rh}{2\pi \: r(h + r)} = 1$

$\bf\implies \:\dfrac{h}{h + r} = 1$

$\bf\implies \:h = h + r$

$\bf\implies \:r = 0$

$\bf\implies \:no \: such \: cylinder \: exist.$

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Might the correct Statement is

Given :-

• The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2.

To find :-

• The ratio between the height and radius of the cylinder.

Solution :-

$\bf\implies \:\dfrac{Curved \: Surface \: Area}{Total \: Surface \: Area} = \dfrac{1}{2}$

$\bf\implies \:\dfrac{2\pi \: rh}{2\pi \: r(h + r)} = \dfrac{1}{2}$

$\bf\implies \:\dfrac{h}{h + r} = \dfrac{1}{2}$

$\bf\implies \:2h = h + r$

$\bf\implies \:h = r$

$\bf\implies \:\dfrac{h}{r} = \dfrac{1}{1}$

$\bf\implies \:h : r \: = 1 : 1$

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