Question

The total surface area of cone is 300picmsqure and its diameter is 24cm.Find the slant height of cone.​

Answer 1

Given :

• Total surface area of the cone = 300 π cm²

• Diameter of the cone = 24 cm

To find :

The slant height of the cone.

Solution :

To find the slant height of the cone , first we have to find the height of the cone.

We know that :

• Formula for Total surface area of cone :

$:\implies \bf{A = \pi r(r + l)}$

Where :

• A = Total surface area
• r = Radius
• l = Slant height

• Formula for radius :

$:\implies \bf{R = \dfrac{D}{2}}$

Where :

• R = Radius
• D = Diameter

Now putting the formula for Radius in the Formula for Total surface of the cone , we get :

$\boxed{\bf{A = \pi \dfrac{D}{2}\bigg(\dfrac{D}{2} + l\bigg)}}$

Now using the formula and substituting the values in it, we get :

$:\implies \bf{300\pi = \dfrac{22}{7} \times \dfrac{24}{2}\bigg(\dfrac{24}{2} + l\bigg)}$

$:\implies \bf{300\pi = \dfrac{22}{7} \times 12 \times (12 + l)}$

$:\implies \bf{300\pi = \dfrac{22}{7} \times 12 \times (12 + l)}$

$:\implies \bf{300\pi = \dfrac{22}{7} \times 144 + 12l}$

$:\implies \bf{300\pi = \dfrac{22}{7} \times 144 + 12l}$

$:\implies \bf{300 \times \dfrac{22}{7} = \dfrac{22}{7} \times 144 + 84l}$

$:\implies \bf{300 \times \dfrac{22}{\not{7}} = \dfrac{22}{\not{7}} \times 144 + 12l}$

$:\implies \bf{300 \times 22 = 22 \times 144 + 12l}$

$:\implies \bf{300 = 144 + 12ll}$

$:\implies \bf{300 - 144 = 12l}$

$:\implies \bf{156 = 12l}$

$:\implies \bf{\dfrac{156}{12} = l}$

$:\implies \bf{13 = l}$

$\boxed{\therefore \bf{Slant\:Height\:(l) = 13\:cm}}$

Hence,the slant height of the cone is 13 cm.