JEE Mains · Maths · STD 12 - 6. Application of derivatives
A square piece of tin of side \(30\,cm\) is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in \(cm ^2\) ) is equal to \(............\).
- A \(675\)
- B \(1025\)
- C \(800\)
- D \(900\)
Answer & Solution
Correct Answer
(C) \(800\)
Step-by-step Solution
Detailed explanation
Volume \(( V )= x (30-2 x )^2\) \(\frac{d V}{d x}=(30-2 x)(30-6 x)=0\) \(x =5\,cm\) Surface area \(=4 \times 5 \times 20+(20)^2=800\,cm ^2\)
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