Question

The dimensions of a cuboid are 44 cm , 21 cm , 12 cm. It is melted and a cone of 24 cm is made.

So,find the radius of its base.


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Answer 1

Answer :

The radius of its base is 21 cm.

Step-by-step explanation :

Dimensions of cuboid ;

Length = 44 cm.

Breadth = 21 cm

Height = 12 cm

Volume of cuboid = l × b × h

⇒( 44 × 21 × 12 ) cm³

⇒ 11088 cm³

It is given that the volume of cuboid is equal to the volume of cone.

Volume of cone = 11088

⇒ π r ² h / 3 = 11088

⇒ 22 / 7 × r² × 8 = 11088

⇒ r² = 11088 × 7 / 22 × 8

⇒ r² = 441

⇒ r = √441

⇒ r = 21 cm.

Hence, the radius is 21 cm.

Answer 2

$\sf {Here's \: the \: answer}$

Answer of the question is $\bf {21 cm }$

Let's see how it came =>


Step by step explanation of the answer =>

Given -

Length of cuboid ( L ) => 44 cm

Breadth ( b )=> 21 cm

Height ( h ) => 12 cm

Height of the cone given ( h1 )=> 24 cm

Solution =>

Let the radius of the cone be r.

As the cuboid is melted and a cone is made,

Volume of cuboid = Volume of cone

$\therefore\sf{L \times b \times h = \frac{1}{3} \times \pi \: r {}^{2} h_{1}}$

$\sf{44 \times 21 \times 12 = \frac{1}{3} \times \frac{22}{7} \times r {}^{2} \times 24}$

$\sf{r {}^{2} = \frac{44 \times 21 \times 12 \times 3 \times 7}{22 \times 24}}$

$\sf{r {}^{2} = 21 \times 21}$

Taking square root on both sides ,

$\sf{r = 21}$

Thus,

The radius of the base is 21 cm.

Thanks!!