Question

A solid metallic cylinder of base radius 11 cm and height 12 cm is melted to form cones, each of height 1 cm and base radius 6 mm. Find the number of cones?

Answer 1

ANSWER:

12100 cones can be made.

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GIVEN:

CYLINDER:

r = 11 cm

h = 12 cm

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CONE:

H = 1 cm

R= 6 mm = 0.6 cm

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TO FIND:

Number of cones(n).

FORMULAE:

VOLUME OF CYLINDER = n × VOLUME OF CONE

EXPLANATATION:

π r² h = n ×( 1/3 π R² H)

Cancel π on both sides.

r² h = n/3 R² H

(11)² × 12 × 3 = n × (0.6)² × 1

n = 121 × 36/0.36

Multiply by 100 on numerator and denominator.

n = 121 × 36 × 100/36

n = 12100

12100 cones can be made.

Answer 2

Given :-

$\sf{\underline{\underline{Clyinder}}}$

• Height (H) = 12cm

• Radius (R) = 11cm

$\sf{\underline{\underline{Cone}}}$

• Height (h) = 1cm

• Radius (r) = 6mm = 0.6 cm

Answer :-

• 12100 Cones

Concept Used :-

$\sf{\boxed{\boxed{No.\:of\:Cones=\dfrac{Volume\:of\:Clyinder}{Volume\:of\:Cone}}}}$

• First of all, convert radius of cone into cm (6mm = 0.6cm)

Explanation :-

We how to find number of cones which are formed by the melting of cylinder . The dimensions of both (cylinder and cones) are given.

$\sf{N=\dfrac{Volume\:of\:Clyinder}{Volume\:of\:Cone}}$

Here $\bf\red N = No.\: of\: Cones$

$\sf{N=\dfrac{Volume\:of\:Clyinder}{Volume\:of\:Cone}}$

$\sf{N=\dfrac{\pi\ R^{2}H}{\dfrac{1}{3}\pi\ r^{2}h}}$

$\sf{N=\dfrac{\cancel{\pi}\times\ 11^{2}\times12}{\dfrac{1}{3}\cancel{\pi}\times\ (0.6)^{2}\times1}}$

$\sf{N=\dfrac{121\times12\times3}{0.36}}$

$\sf{N=\dfrac{121\times\cancel{36}\times100}{\cancel{36}}}$

$\sf{N=12100}$

So, Number of cones are 12100

$\sf{\blue{\underline{\underline{Important}}}}$

$\implies$Volume of Cone = $\sf{\dfrac{1}{3}\pi\ r^{2} h}$

$\implies$Volume of Clyinder = $\sf{\pi\ r^{2}h}$

$\implies$If one shape is converted into another shape without removing any part then the volume of both will be same