Application of derivatives class 12 ex-6.1 NCERT |
Application of derivative lecture - 2 here we will discuss Questions of Ex-6.1 Q.no-1 to 9 in detail.
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#exercise 6.1
1.Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm (b) r = 4 cm
2. The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the
surface area increasing when the length of an edge is 12 cm?
3. The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate
at which the area of the circle is increasing when the radius is 10 cm.
4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the
volume of the cube increasing when the edge is 10 cm long?
5. A stone is dropped into a quiet lake and waves move in circles at the speed of
5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is
the enclosed area increasing?
6. The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of
increase of its circumference?
7. The length x of a rectangle is decreasing at the rate of 5 cm/minute and the
width y is increasing at the rate of 4 cm/minute. When x = 8cm and y = 6cm, find
the rates of change of (a) the perimeter, and (b) the area of the rectangle.
8. A balloon, which always remains spherical on inflation, is being inflated by pumping
in 900 cubic centimetres of gas per second. Find the rate at which the radius of
the balloon increases when the radius is 15 cm.
9. A balloon, which always remains spherical has a variable radius. Find the rate at
which its volume is increasing with the radius when the later is 10 cm.
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