Question

the height of the cone is 16and diameter of the base is 24.find the lateral surface area of the cone and the volume of the cone​

Answer 1

Answer :

• Lateral surface area of cone is 753.6cm²
• Volume of cone is 2413.7cm³

Given :

• Height of the cone is 16cm
• Diameter of the base is 24cm

To find :

• Lateral surface area of cone
• Volume of cone

Solution :

First we need to find the radius

Diameter is 24cm

As we know that

• Radius = Diameter/2

》Radius = 24/2

》Radius = 12cm

• Height is 16cm
• Radius is 12cm

Let the slant height be l

As we know that

• l² = h² + r²

》l² = h² + r²

》l² = (16)² + (12)²

》l² = 256 + 144

》l² = 400

》l = √400

》l = 20cm

Now we have to find the lateral surface area of cone :

We know that,

• Lateral surface area of cone = πrl

Where , r is radius

》Lateral surface area of cone = πrl

》22/7 × 12 × 20

》753.6cm²

Hence , Lateral surface area of cone is 753.6cm²

Now , Volume of cone :

• Volume of cone = 1/3 πr²h

》Volume of cone = 1/3 πr²h

》1/3 × 22/7 × (12)² × 16

》2413.7 cm³

Hence , Volume of cone is 2413.7cm³

Answer 2

Given:-

• Height of the cone = 16cm

• Diameter of the base = 24cm

To Find:-

• It's Lateral Surface Area and Volume

Formula used:-

• ${\boxed{LSA\:of\:Cone=πrl}}$

• ${\boxed{Volume\:of\:Cone=\dfrac{1}{3}πr^2h}}$

Solution:-

Radius = Diameter/2 = 24/2 = 12cm

For Slant Height,

$\implies\:l=\sqrt{r^2+h^2}$

$\implies\:l=\sqrt{12^2+16^2}$

$\implies\:l=\sqrt{144+256}$

$\implies\:l=\sqrt{400}$

$\implies\:l=20cm$

Now,

$\implies\:LSA\:of\:Cone=πrl$

$\implies\:LSA\:of\:Cone=\dfrac{22}{7}\times\:12\times\:20$

${\boxed{\implies\:LSA\:of\:Cone=\dfrac{5280}{7}cm^2}}$

or,

${\boxed{\implies\:LSA\:of\:Cone=754.28cm^2}}$

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Now,

$\implies\:Volume\:of\:Cone=\dfrac{1}{3}πr^2h$

$\implies\:Volume\:of\:Cone=\dfrac{1}{3}\times\:\dfrac{22}{7}\times\:12^2\times\:16$

$\implies\:Volume\:of\:Cone=\dfrac{50688}{21}$

${\boxed{\implies\:Volume\:of\:Cone=\dfrac{16896}{7}cm^3}}$

or,

${\boxed{\implies\:Volume\:of\:Cone=2413.71cm^3}}$

Hence, The Lateral Surface Area of cone is 754.28cm² and it's volume is 2413.71cm³.

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