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Question

Find the volume, curved surface area and the total surface area of a cone having base radius $$35\ cm$$ and height $$12\ cm$$.


Solution

It is given that

Radius of the cone $$=35\ cm$$

Height of the cone $$=12\ cm$$

We know that

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

By substituting the values

Volume of the cone $$=\dfrac{1}{3}\times \dfrac{22}{7}\times 35^{2}\times 12$$

On further calculation

Volume of the cone $$=15400\ cm^{2}$$

We know that 

Slant height $$l=\sqrt {(r^{2}+h^{2})}$$

By substituting the values

$$l=\sqrt{ (35^{2}+12^{2})}$$

On further calculation

$$l=\sqrt{ 1369}$$

So we get

$$l=37\ cm$$

We know that 

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

By substituting the values

Total surface area of cone $$=\dfrac{22}{7}\times 35\times (37+35)$$

On further calculation 

Total surface area of cone $$=22\times 5\times 72$$

So we get

Total surface area of cone $$=7920\ cm^{2}$$

Mathematics
RS Agarwal
Standard IX

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