TS EAMCET · Maths · Application of Derivatives
The radius of a cone of height 9 units is changed from 2 units to 2.12 units. The exact change and approximate change in the volume of the cone are respectively
- A \((1.4437) \pi,(1.44) \pi\)
- B \((1.4832) \pi,(1.479) \pi\)
- C \((1.4842) \pi,(1.48) \pi\)
- D \((1.4832) \pi,(1.44) \pi\)
Answer & Solution
Correct Answer
(D) \((1.4832) \pi,(1.44) \pi\)
Step-by-step Solution
Detailed explanation
\( V = \frac{1}{3} \pi r^2 h \) \( V_1 = \frac{1}{3} \pi (2^2) (9) = 12 \pi \) \( V_2 = \frac{1}{3} \pi (2.12^2) (9) = 13.4832 \pi \) \( \Delta V_{\text{exact}} = V_2 - V_1 = 13.4832 \pi - 12 \pi = 1.4832 \pi \)…
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