Question

(2) The base radius and height of a solid metal cylinder are 12 centimetres
and 20 centimetres. By melting it and recasting, how many cones of
base radius 4 centimetres and height 5 centimetres can be made?​

Answer 1

$\large\underline{\boxed{\bold\red{Question}}}$

A solid metal cylinder is of base-radius 12 centimetres and height 20 centimetres. By melting and recasting, how many cones of base-radius 4 centimetres and height 5 centimetres can be made?

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$\large\underline{\boxed{\bold\blue{Answer}}}$

$\large\underline{\boxed{\bold\purple{Given}}}$

$\large\pink{Base \: radius \: of \: cylinder = 12cm}$

$\large\pink{Height \: of \: the \: cylinder = 20cm}$

$\large\pink{Base \: radius \: of \: cone = 4cm}$

$\large \pink{ Height \: of \: cone = 5cm}$

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$\large\green{Volume \: of \: cylinder = πr²h}$

$\large\orange{:\leadsto \pi×12×12×20}$

$\huge\orange{\boxed{2880π \: cm³}}$

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$\green{Volume \: of \: cone = \dfrac{1}{3}πr²h}$

$\orange{:\leadsto \dfrac{1}{3} \times \pi \times 4 \times 4 \times 5}$

$\large\orange{\boxed{\dfrac{80π}{3} \: cm³}}$

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$\green{Volume \: of \: cones = \dfrac{Volume \: of \: cylinder}{volume \: of \: cone}}$

$\orange{ :\leadsto \dfrac{2880 \: \pi}{\dfrac{80 \: \pi}{3}}}$

$\orange{: \leadsto\dfrac{3 \times \cancel{288}\cancel{0} \: \cancel{\pi}}{\cancel8\cancel{0} \: \cancel{\pi}}}$

$\large\orange {: \leadsto3 \times 36}$

$\huge\boxed{\orange{108}}$

Therefore, 108 cones can be made from given cylinder.

[Hope this helps you.../]

Answer 2

Answer:

108 cones of base radius 4 cm and the height 5 cm can be made from the metal cylinder.

Step-by-step explanation:

Given:

The base radius (r) of the cylinder = 12 cm

Height (h) of the cylinder = 20 cm

The base radius of the cone that wants to be made = 4 cm

Height of the cone = 5 cm

To find out:

How many cones can be made from the cylinder

Solution:

To find the solution we want to find the volume of one cone and the cylinder. And dividing the volume of the cylinder by the volume of a cone, we can find how many cones can be made.

The volume of the cylinder ⇒

It can be found by the following formula,

    V = πr²h

By substituting the values we get,

    V = 3.14 × 12² × 20                < π = 3.14>

       = 9043.2 cm³

The volume of a cone ⇒

 The formula to find the volume of a cone is given as,

        $V=\dfrac{\pi r^2 h}{3}$

By substituting the values,

       $V=\dfrac{3.14 \times 4^2 \times 5}{3}$

          = 83.74 cm³

⇒ Now divide the volume of the cylinder by the volume of the cone. Therefore,

       $\dfrac{9043.2}{83.74} = 108$

Hence, 108 cones can be made from the metal cylinder.