Question

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Question:-

The radius of the base of the solid right cylinder is 4 cm and its height 7 cm. On melting this solid cylinder how many right circular cylinder of radius 2 cm and height
$3 \times \frac{1}{2}$
cm can be made.

Note:-

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Answer 1

$\bf\huge\underline{Answer :-}$

Given :

• Radius of the base of bigger cylinder (R) = 4 cm
• Height of the bigger cylinder (H) = 7 cm
• Radius of smaller cylinder (r) = 2 cm
• Height of smaller cylinder (h) = (3 × 1/2) cm

To find :

• Number of smaller cylinders than can be made by melting the bigger cylinder.

Solution :

Volume of bigger cylinder = πR²H cu. unit

= π × (4)²× 7 cm³

= (π × 16 × 7) cm³

Volume of smaller cylinder = πr²h cu. unit

= π × (2)²× 3/2 cm³

= (π × 4 × 3 1/2) cm³

[We can find the number of smaller cylinders to be made by melting the bigger cylinder by dividing the volume of bigger cylinder by the volume of smaller cylinder.]

$\sf\longrightarrow No. \: of \: smaller \: cylinders \: = \: \dfrac {\pi {R}^{2}H}{\pi {r}^{2}h}$

$\sf\longrightarrow \: \: \: \: \: \: \: \: \dfrac{\pi \times 16 \times 7}{\pi \times 4 \times \frac{7}{2}}$

$\sf\longrightarrow \: \: \: \: \: \: \: \: \dfrac{\cancel{\pi} \times 16 \times 7}{\cancel{\pi} \times 4 \times \frac{7}{2}}$

$\sf\longrightarrow \: \: \: \: \: \: \: \: \dfrac{16 \times 7}{4 \times \frac{7}{2}}$

$\sf\longrightarrow \: \: \: \: \: \: \: \: \dfrac{\cancel{112}}{\cancel{14}}$

$\sf \: \: \: \: \: \: \: \: \therefore 8$

Hence, the number of smaller cylinders that can be made is 8.

Answer 2

Answer:

Given :-

• Radius of base of solid right cylinder = 4 cm
• Height = 7 cm
• On melting, how many cylinder of radius 2 cm and height 3 × ½ cm

To Find :-

Total cylinder may made

Solution :-

At first finding volume of both cylinder

Let the volume of Cylinder 1 be V and Cylinder 2 be V'

V = πr²h

V = π (4)² × 7

V = π 16 × 7 cubic units

V' = πr²h

V' = π × (2)² × 3½

V' = π × 4 × 7/2 cm

Now

Finding Total Cylinder

$\sf \: Total \: Cylinder = \dfrac{\pi \: R{}^{2} h}{\pi {r}^{2} h}$

Now,

Putting Value

$\sf \: Total \: Cylinder = \dfrac{\pi \times \: 16 \times 7}{\pi \: \times 4 \times \frac{7}{2} }$

$\sf \: Total \: Cylinder = \dfrac{ \cancel\pi \times 16 \times 7}{ \cancel \pi \: \times 4 \times \frac{7}{2} }$

$\sf \: Total \: Cylinder = \dfrac{16 \times 7}{4 \times \frac{7}{ 2} }$

$\sf \: Total \: Cylinder = \dfrac{16 \times 7}{ \cancel{4} \: \times \frac{7}{ \cancel2} }$

$\sf \: Total \: Cylinder = \dfrac{16 \times 7}{ 2 \times 7}$

$\sf \: Total \: Cylinder = \dfrac{112}{14}$

$\sf \: Total \: Cylinder = 8$