Question

Ratio of CSA and TSA of cylinder is 4:7 find out the ratio of the height and radius of the cylinder.
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Answer 1

Step-by-step explanation:

Solution:-

The ratio of the radius and height of the cone is 4 : 7.

Let the radius of the cone be 4x and the height be 7x

So,

Curved surface area of the cone = πrl

792 = 22/7*4x*7x

x² = (792*7)/(22*4*7)

x² = 9

x = √9

x = 3 cm

So, the radius of the cone = 4 × 3 = 12 cm.

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Answer 2

ANSWER :-

• Ratio of height and radius is 4:3.

GIVEN :-

• Ratio of CSA and TSA of cylinder is 4:7.

TO FIND :-

• Ratio of height and radius.

TO KNOW :-

★ CSA of cylinder = 2πrh

★ TSA of cylinder = 2πr(r+h)

SOLUTION :-

We know that ratio of CSA and TSA is 4:7.

Let the cylinder is of height 'h' and radius 'r'.

CSA → 2πrh

TSA → 2πr(r+h)

So, according to question ,

$\\ \implies \sf \: \frac{ \cancel{2\pi \: r} \: h}{ \cancel{2\pi \: r}(r + h)} = \frac{4}{7} \\ \\ \implies \sf \: \frac{h}{r + h} = \frac{4}{7} \\ \\ \implies\sf \: 7h = 4(r + h) \\ \\ \implies\sf \: 7h = 4r + 4h \\ \\ \implies \sf \: 7h - 4h = 4r \\ \\ \implies\sf \: 3h = 4r \\ \\ \implies \boxed{\boxed{ \sf \: \frac{h}{r} = \frac{4}{3} }}$

Hence , ratio of height and radius of the cylinder is 4:3.

MORE TO KNOW :-

★ CSA of Cone = 2πrl

★ TSA of Cone = 2πr(r+l)

★ CSA of Cube = 4 × edge²

★ TSA of Cube = 6 × edge²

★ CSA of Cuboid = 2(lh+bh)

★ TSA of Cuboid = 2(lh+bh+lb)