Question

A) A metallic cuboid is of measurements 11 cm. * 15 cm. x 7.5 cm. If it is melted and
recast as a cylinder of height 7 cm. Find the diameter of the cylinder.​

Answer 1

$\huge{\text{\underline{Solution:-}}}$

1) Dimensions of the metal cuboid:-

★ Given:-

• Length = l = 22 cm
• Breadth = b = 15 cm
• Height = h = 7.5 cm

2) Height of the cylinder (H) = 14 cm

Let radius of the cylunder base = r cm

★According to the question:-

Metal Cuboid melted and cast into a cylinder.

Therefore,

Volume of the cylinder = volume of the metal cuboid

$\implies$π × r² × H = lbh

$\implies$22 / 7 × r² × 14 = 22 × 15 × 7.5

$\implies$22 × r² × 2 = 22 × 15 × 7.5

$\implies$r² = ( 22 × 15 × 75 ) / ( 22 × 2 × 10 )

$\implies$r² = 225 / 4

$\implies$r ² = ( 15 /2 )²

$\implies$r = 15 / 2 cm

$\implies\boxed{\tt{r = 7.5 cm}}$

Radius of the cylinder = r = 7.5 cm

So, ATQ we need to find diameter:-

$\implies$d = 2 × radius

$\implies$ 2 × 7.5

$\implies\boxed{\tt{d= 15 cm }}$

Therefore, diameter of the cylinder = 15cm.

_________________________________

Answer 2

Answer:

${\underline{\boxed{\sf\purple{Diameter\: of \: cylinder =15\: cm \: [Approx.] }}}}$

Step-by-step explanation:

Given:-

• Length of cuboid (l) = 11 cm
• Breadth of cuboid (b) = 15 cm
• Height of cuboid (h) = 7.5 cm
• Height of cylinder (H) = 7 cm

To find:-

• Diameter of cylinder (d)= ?

When metalic cuboid is melted and recast as a cylinder,then volume of cuboid = Volume of cylinder.

We know that,

$\implies{\boxed{\sf\green{Volume \: of \: cylinder = \pi{r}^{2}h }}}$

$\implies{\boxed{\sf\green{Volume \: of \: cuboid = lbh}}}$

$\because\sf Volume \: of \: cylinder = Volume \: of \: cuboid$

$\implies\sf \pi{r}^{2}H = lbh \\\\\implies\sf \dfrac{22}{\cancel{7}}\times {r}^{2} \times \cancel{7} = 11 \times 15 \times 7.5 \\\\\implies\sf 22{r}^{2} = 1237.5 \\\\\implies {r}^{2} =\dfrac{1237.5}{22} \\\\\implies\sf {r}^{2} = 56.25 \\\\\implies\sf r =\sqrt{56.25} \\\\\implies{\underline{\boxed{\sf\green{r = 7.5 \: cm \: \: [Approx.]}}}}$

$\rule{200}{1}$

$\implies\sf Diameter = 2 \times radius \\\\\implies\sf Diameter = 2 \times 7.5 \\\\\implies{\underline{\boxed{\sf\green{Diameter = 15 \: cm \: \:[Approx.]}}}}$

${\underline{\boxed{\therefore{\sf\pink{Diameter\: of \: cylinder = 15 \: cm [Approx.]}}}}}$