Question

The dimensions of a cuboid are 44 cm 21 cm 12 cm it is method and a cone of height 24 cm is made find the radius of its base

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

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

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The radius of it's base.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the radius of cone be r

We know that formula of the volume of cuboid :

$\bf{\boxed{\bf{Volume\:=Length\times breadth\times height\:\:\:\:(cubic\:unit)}}}}}$

$\bf{We\:have}\begin{cases}\sf{Length\:of\:cuboid\:(l)=44cm}\\ \sf{Breadth\:of\:cuboid\:(b)=21cm}\\ \sf{Height\:of\:cuboid\:(h)=12cm}\\ \sf{Height\:of\:cone\:(h)=24cm}\end{cases}}$

We know that formula of the volume of cone :

$\bf{\boxed{\bf{Volume\:=\frac{1}{3} \pi r^{2}h \:\:\:(cubic\:unit)}}}}}$

A/q

$\longrightarrow\sf{Volume\:of\:cone=Volume\:of\:cuboid}\\\\\\\longrightarrow\sf{\dfrac{1}{\cancel{3}} \times \dfrac{22}{7} \times r^{2} \times \cancel{24}=44\times 21\times 12}\\\\\\\longrightarrow\sf{\dfrac{22}{7} \times r^{2} \times 8=11088}\\\\\\\longrightarrow\sf{\dfrac{176}{7} \times r^{2}=11088 }\\\\\\\longrightarrow\sf{r^{2}=\dfrac{\cancel{11088} \times 7}{\cancel{176}} }\\\\\\\longrightarrow\sf{r^{2} =63\times 7}\\\\\\\longrightarrow\sf{r^{2} =441}$

$\longrightarrow\sf{r=\sqrt{441} }\\\\\\\longrightarrow\sf{\pink{r=21\:cm}}$

Thus;

The radius of it's base r = 21 cm .

Answer 2

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$\tt{\huge{\purple{ ..................... }}}$

QUESTION -

The dimensions of a cuboid are 44 cm 21 cm 12 cm it is method and a cone of height 24 cm is made find the radius of its base.

SOLUTION -

From the above question, we can gather the following information....

The dimensions of a cuboid are 44 cm 21 cm 12 cm it is method and a cone of height 24 cm is made.

Volume Of Cuboid :

The volume of the Cuboid is equal to the product of it's length , breadth and height.

Volume = LBH = 44 cm × 21 cm × 12 cm

=> Volume = 11088 Cubic cm.

Now we know that :

Volume Of Cuboid = Volume Of Cone.

We know that :

Volume of a cone = ( 1 / 3 ) π { r } ^ 2 H

So,

We have :

H = 24 cm

Volume Cone = 8 π r ^ 2

=> 8 π r ^ 2 = 11088

=> π r ^ 2 = 1386

=> r ^ 2 = { 1386 × 7 } / 22 = 63 × 7

=> r = 7 × 3 = 21 cm.

Hence the required radius of the cone is 21 cm.

ANSWER -

Hence the required radius of the cone is 21 cm.

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