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.
Last updated date: 23rd Mar 2023
•
Total views: 306.6k
•
Views today: 3.86k
Answer
306.6k+ 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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
