The height of a cone increases by `k %` its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that `k` is small?

Explanation

Therefore,

` frac{Delta h}{h}=frac{Delta r}{r}=frac{Delta l}{l} `

Also, ` frac{Delta h}{h} times 100=k `

Then, `frac{Delta h}{h} times 100=frac{Delta r}{r} times 100=frac{Delta l}{l} times 100=k . .(1) `


(i) Total surface area of the cone, `T=pi r l+pi r^{2}`

Differentiating both sides w, r, t, r, we get

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