CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the volume curved surface area and the total surface area of a cone whose height is $$6\ cm$$ and slant height $$100\ cm$$ (Take $$\pi=3.14$$)


Solution

It is given that
Height of the cone $$=6\ cm$$
Slant height of the cone $$b=10\ cm$$

We know that

Radius of the cone $$=\sqrt {(l^{2}-h^{2})}$$

By substituting the values

Radius of the cone $$\sqrt {(10^{2}-6^{2})}$$

On further calculation

Radius of the cone $$\sqrt{ (100-36)}=\sqrt{ 64}$$

So we get

Radius of the cone $$=8\ cm$$

We know that

Volume of the cone $$=\dfrac{1}{3}\pi r^{2}h$$

By substituting the values

Volume of the cone $$=\dfrac{1}{3}\times 3.14\times 8^{2}\times 6$$

On further calculation

Volume of the cone $$=401.92\ cm^{2}$$

We know that 

Curved surface area of a cone $$=\pi rl$$

By substituting the values

Curved surface area of a cone $$=3.14\times 8\times 10$$

So we get

Curved surface area of a cone $$=251.2\ cm^{2}$$

We know that

Total surface area of cone $$=\pi r(l+r)$$

By substituting the values

Total surface area of cone $$=3.14\times 8\times (10+8)$$

On further calculation

Total surface area of cone $$=3.14\times 8\times 18$$

So we get

Total surface area of cone $$=424.16\ cm^{2}$$

Mathematics
RS Agarwal
Standard IX

Suggest Corrections
thumbs-up
 
2


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image