Math, asked by BrainlyHelper, 1 year ago

If a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

Answers

Answered by nikitasingh79
5

Answer:

The volume of two parts of the cone is 1 : 7 .

Step-by-step explanation:

SOLUTION :  

Let r & R be the radius of the lower part of the frustum.

Height of a cone , AB’ = 10 cm

Height of a Smaller cone, AB = 5 cm

[Cut through the midpoint of its height]

From the figure,  

AB = h = 5

AB’ = 2h = 10

BC = r  

B'C = R

In ∆ABC & ∆AB’C’ ,

∠ABC = ∠AB’C’ (each 90°)

∠ACB = ∠AC’B’ (corresponding angles)

∆ABC ∼ ∆AB’C’ [By AA Similarity]

BC/B'C’ = AB/AB’

[Corresponding sides of a similar triangles are proportional]

r/R = 5 /10

r/R = ½

R = 2r

Volume of the upper part (Smaller cone) = ⅓ πr²h

Volume of solid cone = ⅓ π R²2h

= ⅓ π (2r)² 2h = ⅓ π × 4r² × 2h

Volume of solid cone = 8/3πr²h

Volume of lower part (frustum) = volume of solid cone - volume of Smaller cone  

= 8/3πr²h - ⅓ πr²h = 7/3 πr²h

Volume of lower part (frustum) = 7/3 πr²h

Volume of the upper part (Smaller cone)/ Volume of lower part (frustum) =   ⅓ πr²h / 7/3 πr²h

= 1/7  

Hence, the ratio of volume of two parts of the cone is 1 : 7 .

HOPE THIS ANSWER WILL HELP YOU….

Attachments:
Answered by Harshikesh16726
1

Answer:

Volume of cone=

3

1

πr

1

2

h

1

=

3

1

π(

2

r

)

2

×

2

h

=

3

1

π(

2

10

)

2

×

2

h

=

6

25πh

cm

3

Volume of frustum ABCD=

3

1

πh

2

(R

2

+r

2

+Rr)

=

3

1

π×

2

h

(10

2

+5

2

+10×5)

=

6

175πh

Required ratio=

6

175πh

6

25πh

=

175

25

=

7

1

  1. =1:7

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