Question

the height of a right circular cone is 9 CM if its volume is 432 cm cube What is the slant height of the cone​

Answer 1

Given :

• Height of the cone → 9 cm
• Volume → 432 cm³

To Find :

• Slant Height of cone

Solution :

Since we are provided with the volume of the cone, let's apply the formula of volume of cone.

Formula :

$\large{\boxed{\mathtt{\red{Volume_{cone}\:=\:{\dfrac{1}{3}\:\pi\:r^2\:h}}}}}$

➣ $\mathtt{432\:=\:{\dfrac{1}{3}\:\times\:{\dfrac{22}{7}\:r^2\:9}}}$

➣ $\mathtt{432\:=\:{\dfrac{22}{21}\:\times\:r^2\:9}}$

➣ $\mathtt{432\:=\:{\dfrac{198}{21}\:\times\:r^2}}$

➣ $\mathtt{432=\:9.42\:r^2}$

➣ $\mathtt{\dfrac{432}{9.42}\:=\:r^2}$

➣ $\mathtt{45.85\:=\:r^2}$

➣ $\mathtt{\sqrt{45.85}\:=\:r^2}$

➣ $\mathtt{6.77\:=r}$

$\large{\boxed{\mathtt{\red{Radius\:=r\:=\:6.77\:cm}}}}$

Slant height, l :

➣ $\mathtt{l^2\:=\:r^2\:+\:h^2}$

➣ $\mathtt{l^2\:=\:(6.77)^2\:+\:(9)^2}$

➣ $\mathtt{l^2\:=\:45.83\:+\:81}$

➣ $\mathtt{l^2\:=\:126.83}$

➣ $\mathtt{l\:=\:{\sqrt{126.83}}}$

➣ $\mathtt{l\:=\:11.26\:}$

$\large{\boxed{\rm{\purple{Slant\:height\:=\:l\:=10cm\:(approx)}}}}$