# The length, breadth and height of a solid metallic cuboid are $44cm,21cm$ and $12cm$ respectively. It is melted and a solid cone is made out of it. If the height of the cone is$24cm$, then find the diameter of its base.

Answer

Verified

363.6k+ views

Hint: When something is melted and converted to another shape then its volume will not change.

The problem statement says, the cuboid is melted so the hack here is, volume will not be changed. So, the volume of cuboid will be equal to the volume of solid cone. We know that, Volume of cuboid$ = l \times b \times h$where,$l = length,b = breath\;{\text{and }}h = height$. Also, volume of cone$ = \dfrac{1}{3}\pi {r^2}h$.

Here we have given length, breadth and height of a solid metallic cuboid and height of the cone. The only remaining unknown in both the volume formulas is radius. Let’s calculate it.

$

l \times b \times h = \dfrac{1}{3}\pi {r^2}h \\

\Rightarrow 44 \times 21 \times 12 = \dfrac{1}{3} \times \dfrac{{22}}{7}{r^2} \times 24{\text{ }}[l = 44cm,b = 21cm,{h_{cuboid}} = 12cm,{h_{cone}} = 24cm] \\

\Rightarrow 44 \times 21 = \dfrac{1}{3} \times \dfrac{{22}}{7}{r^2} \times 2 \\

\Rightarrow 21 = \dfrac{1}{3} \times \dfrac{{{r^2}}}{7} \\

\Rightarrow {r^2} = 21 \times 3 \times 7 \\

\Rightarrow {r^2} = 21 \times 21 \\

\Rightarrow r = 21cm \\

$

But we need to find diameter. So, we’ll use$d = 2r$. That is$d = 2 \times 21 = 42cm$.

Hence the required diameter of the cone is$42cm$.

Note: The hack here in this question was to understand, when something is melted and converted to another shape then its volume will not change then using the correct formula will lead us to the answer.

The problem statement says, the cuboid is melted so the hack here is, volume will not be changed. So, the volume of cuboid will be equal to the volume of solid cone. We know that, Volume of cuboid$ = l \times b \times h$where,$l = length,b = breath\;{\text{and }}h = height$. Also, volume of cone$ = \dfrac{1}{3}\pi {r^2}h$.

Here we have given length, breadth and height of a solid metallic cuboid and height of the cone. The only remaining unknown in both the volume formulas is radius. Let’s calculate it.

$

l \times b \times h = \dfrac{1}{3}\pi {r^2}h \\

\Rightarrow 44 \times 21 \times 12 = \dfrac{1}{3} \times \dfrac{{22}}{7}{r^2} \times 24{\text{ }}[l = 44cm,b = 21cm,{h_{cuboid}} = 12cm,{h_{cone}} = 24cm] \\

\Rightarrow 44 \times 21 = \dfrac{1}{3} \times \dfrac{{22}}{7}{r^2} \times 2 \\

\Rightarrow 21 = \dfrac{1}{3} \times \dfrac{{{r^2}}}{7} \\

\Rightarrow {r^2} = 21 \times 3 \times 7 \\

\Rightarrow {r^2} = 21 \times 21 \\

\Rightarrow r = 21cm \\

$

But we need to find diameter. So, we’ll use$d = 2r$. That is$d = 2 \times 21 = 42cm$.

Hence the required diameter of the cone is$42cm$.

Note: The hack here in this question was to understand, when something is melted and converted to another shape then its volume will not change then using the correct formula will lead us to the answer.

Last updated date: 29th Sep 2023

•

Total views: 363.6k

•

Views today: 10.63k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

What is the basic unit of classification class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers