Question

7. The radii of two cylinders are in the ratio 3:4 and their heights are in the ratio 5:3. Find the ratio of their curved surface areas​

Answer 1

Given

• Radii of two cylinders are in the ratio 3:4
• Heights of the two cylinders are in the ratio 5:3

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To Find

• The ratio of their curved surface areas

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Solution

CSA of cylinder = 2πrh

Consider the radii of the 1st cylinder to be '3r' and the radii of the 2nd cylinder to be '4r' since they are in the ratio 3:4. Also, consider the height of the 1st cylinder to be '5h' and the height of the 2nd cylinder to be '3h' since they are in the ratio of 5:3.

Cylinder 1

Radii = 3r

Height = 5h

CSA of cylinder = 2πrh

CSA of cylinder 1 = 2π × 3r × 5h

CSA of cylinder 1 = 2π × 15rh

CSA of cylinder 1 = 30πrh square units

∴ CSA of the 1st cylinder is 30πrh square units.

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Cylinder 2

Radii = 4r

Height = 3r

CSA of cylinder = 2πrh

CSA of cylinder 2 = 2π × 4r × 3h

CSA of cylinder 2 = 2π × 12rh

CSA of cylinder 2 = 24πrh square units

∴ CSA of the 2nd cylinder is 24πrh square units.

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Ratio of the curved surface areas = CSA of 1st Cylinder : CSA of 2nd Cylinder  

⇒ 30πrh : 24πrh

$\implies \dfrac{30\pi rh}{24\pi rh}$

$\implies \dfrac{30}{24}$

$\implies \dfrac{5}{4}$

∴ The ratio of their curved surface areas is 5:4

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Answer 2

PROVIDED INFORMATION :-

★ radii of two cylinders are in the ratio 3:4

heights are in the ratio 5:3

TO FIND :-

★Find the ratio of their curved surface areas = ?

Using concept :-

★ formula to find curved surface area = 2 π rh

UNDERSTANDING THE CONCEPT :-

★ this question is telling about the chapter Surface Areas and Volumes we have provided radii of two cylinders are in the ratio 3:4 heights are in the ratio 5:3 first we have to multiply 2 with 3 with 5 then, we will multiply 2 with 4 with 3 then, we get the answer

what is volume ?

★ Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre i.e. m³.

what is surface area ?

★ Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

QUESTION :-

★ The radii of two cylinders are in the ratio 3:4 and their heights are in the ratio 5:3. Find the ratio of their curved surface areas

SOLUTION :-

STEP 1 :

Consider the radius of the two cylinders

to be 3R and 4R.

And their heights be 5H and 3H

★ Let the radii of the cylinder be 3x, 4x and their hights be 5y, 3y respectively.

★ Then, Ratio of their curved surface

★ area = 2 π × 3 x × 5 y / 2π × 4x × 3y

then, we multiply we get :

★= 5/4 = 5:4

Hence, Curved surface are a ratio is 5:4