CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q222 Marksrelated_rates
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 22 (Applications Of Derivatives)
A spherical balloon’s volume grows at 20 cm³/s. Find its surface-area rate at radius 4 cm. OR Find increasing intervals of x³+2x²−1.
Alternative 1 2 Marks
A spherical balloon’s volume grows at 20 cm³/s. Find its surface-area rate at radius 4 cm.
Answer: 10 cm²/s.
- Use dV/dt=4πr² dr/dt.
- Then dA/dt=8πr dr/dt=(2/r)dV/dt.
- At r=4 this equals 10.
Alternative 2 2 Marks
Find increasing intervals of x³+2x²−1.
Answer: (−∞,−4/3] and [0,∞).
- The derivative is x(3x+4).
- Its sign is positive below −4/3 and above 0.
- These give the two increasing intervals.