Question

A Metallic cuboid is of Dimensions 11cm x12cm
x 2.5cm was melted and cast into a
Cylinder of height 100cm, what is its radius?
​

Answer 1

Answer:

Given :-

• A metallic cuboid of dimensions 11 cm × 12 cm × 2.5 cm was melted and cast into a cylinder of height is 100 cm.

To Find :-

• What is the radius of cylinder.

Formula Used :-

$\clubsuit$ Volume of Cuboid :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Cuboid =\: Length \times Breadth \times Height}}}$

$\clubsuit$ Volume of Cylinder :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Cylinder =\: {\pi}r^2h}}}$

where,

• r = Radius
• h = Height

Solution :-

First, we have to find the volume of cuboid :

Given :

• Length = 11 cm
• Breadth = 12 cm
• Height = 2.5 cm

According to the question by using the formula we get,

$\implies \sf Volume\: of\: Cuboid =\: 11\: cm \times 12\: cm \times 2.5\: cm$

$\implies \sf Volume\: of\: Cuboid =\: 132\: cm^2 \times 2.5\: cm$

$\implies \sf\bold{\purple{Volume\: of\: Cuboid =\: 330\: cm^3}}$

Hence, the volume of cuboid is 330 cm³.

Now, we have to find the radius of cylinder :

$\mapsto$ It was melted and cast into a cylinder of height is 100 cm.

Then,

$\dashrightarrow \sf\bold{Volume\: of\: Cuboid =\: Volume\: of\: Cylinder}$

Given :

• Height = 100 cm
• Volume of Cuboid = 330 cm³

According to the question by using the formula we get,

$\implies \sf \dfrac{22}{7} \times r^2 \times 100 =\: 330$

$\implies \sf r^2 =\: \dfrac{330 \times 7}{22 \times 100}$

$\implies \sf r^2 =\: \dfrac{231\cancel{0}}{220\cancel{0}}$

$\implies \sf r^2 =\: \dfrac{\cancel{231}}{\cancel{220}}$

$\implies \sf r^2 =\: 1.05$

$\implies \sf r =\: \sqrt{1.05}$

$\implies \sf\bold{\red{r =\: 1.025\: cm}}$

$\therefore$ The radius of cylinder is 1.025 cm .