Question

6. A sphere, a cylinder, a cone have same base and height. Find the ratio of
their CSA.
​

Answer 1

Answer :

• 4 : 4 : √5

Given:

• A sphere , a cylinder , a cone have same base and height

To find:

• ratio of their csa ( curved surface of area )

Solution:

so,

• Height of sphere = diameter (d)

• cone and cylinder have height 2r

As we know that,

• curved surface area of sphere = 4 πr²
• curved surface area of cylinder = 2 πr (2r) = 4πr²
• curved surface area of cone = πrl

Now,

where l = √(r² + h²) = √(r² + 2r²) = √5r² = r√5

• so, curved surface area of cone is π√5r²

Now we have to find the ratio of their curved surface area

ratio of their csa (sphere, cone,cylinder) = 4πr² : 2πrh : πrl

● 4πr² : 2πrh : πrl

● 4πr² : 4πr² : πr²√5

● 4 : 4 : √5

Hence, ratio of their csa is 4 : 4 : √5

Answer 2

Answer:

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.

Then

Curved surface area of Sphere=4πr²

Curved surface area of cylinder =2πr(2r)=4πr²

Curved surface area of cone = πrl

where, l=

(r

2

+h

2

)=

(r2+(2r)

2

)=

5r

2

=r

5

⇒ Curved surface area of cone =π

5r

2

Now,

ratio of CSA 's a sphere ,cylinder and a cone = 4πr

2

:2πrh:πrl

=4πr

2

:4πr

2

:πr

2

5

=4:4:

5

Step-by-step explanation:

Hope this answer will help you✌