Question

the hight of a cone is 9cm it base daimeter is 24cm what is its slant hight and find the total surface area of the cone ​

Answer 1

Answer:

Total surface area of a cone =πr(r+l)

Hence, TSA of this cone, =

7

22

×12×(12+9)=792m

2

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Answer 2

☞ Question :

The height of a cone is 9 cm it base diameter is 24cm. What is its slant height and the total surface area of the cone

☞ To Find :

• The Slant Height of the Cone.

• The Total Surface Area of the Cone.

☞ We Know :

$\bullet\:$Slant Height of a Cone :

$\blue{\sf{\underline{\boxed{l = \sqrt{r^{2} + h^{2}}}}}}$

$\bullet\:$Total Surface Area of a Cone :

$\blue{\sf{\underline{\boxed{TSA = \pi r(r + l)}}}}$

Where,

• l = Slant Height of the Cone

• r = Radius of the Cone

• TSA = Total Surface Area of the Cone

☞ Concept :

To Find the Slant height , we have to Find it's radius of the base of Cone .

Given ,

• Diameter = 24 cm

We know ,

$\sf{Radius = \dfrac{Diameter}{2}}$

Putting the value in it , we get :

$\implies \sf{Radius = \dfrac{24}{2}} \\ \\ \\ \implies \sf{Radius = 12 cm} \\ \\ \\ \therefore \purple{\sf{Radius = 12 cm}}$

Hence , the Radius of the Cone is 12 cm.

Now by the given Height and the found Radius , we can find the Slant Height and the Total Surface Area of the Cone.

☞ Solution :

$\bullet\:$Slant Height of the Cone :

Given :

• Height = 9 cm

• Radius = 12 cm

Using the formula and substituting the values in it , we get :

$\green{\sf{l = \sqrt{r^{2} + h^{2}}}} \\ \\ \\ \implies \sf{l = \sqrt{12^{2} + 9^{2}}} \\ \\ \\ \implies \sf{l = \sqrt{144 + 81}} \\ \\ \\ \implies \sf{l = \sqrt{225}} \\ \\ \\ \implies \sf{l = 15 cm} \\ \\ \\ \therefore \purple{\sf{l = 15 cm}}$

Hence, The Slant Height of the Cone is 15 cm.

$\bullet\:$Total Surface Area of a Cone :

$\green{\sf{TSA = \pi r(r + l)}} \\ \\ \\ \implies \sf{TSA = \dfrac{22}{7} \times 12 \times (12 + 15)} \\ \\ \\ \implies \sf{TSA = \dfrac{22}{7} \times 12 \times 27} \\ \\ \\ \implies \sf{TSA = \dfrac{22}{7} \times 324} \\ \\ \\ \implies \sf{TSA = \dfrac{7128}{7}} \\ \\ \\\implies \sf{TSA = 1018.3 cm^{2}} \\ \\ \\ \therefore \purple{\sf{TSA = 1018.3 cm^{2}}}$

Hence , the Total Surface Area of the Cone is 1018.3 cm².

Additional Information :

• Volume of a Cone = ⅓πr²h

• CSA of a Cone = πrl

• Volume of a Cylinder = πr²h

• CSA of a Cylinder = 2πrh