rate of change

QUESTION 1 :A snowball has volume where r is the radius. The snowball is melting so that at the instant that the radius is 4 cm. The radius is decreasing at the rate of 0 .25 cm/min.
What is the rate of change of the volume at this instant?
FACT
IDEA
LEARNING ISSUE
ACTION PLAN
1) Snowball is melting that at the instant.
2) The snowball radius is 4cm.
3) The radius is decreasing at the rate of 0 .25 cm/min.
1) Make equation using chain rule. Chain rule based on the information given.

1) What is the rate of change of the volume at this instant?
2) How to solve the problem?

http://www.math.tamu.edu/~jlewis/CRA6.4.htm
SOLUTION :
By the chain rule,,
So when r=4 and we have cubic cm/min

QUESTION 2 : A container in the shape of a hollow cone of semi vertical angle of 45 degree is held it’s vertex pointing downwards. The height of container is 0.36m and is filled with water. The water leaks through a small hole through the vertex. If the water sinks at a rate of 0.01m in 120second, and the water continues to leak at the same rate, find the rate at which the water level is sinking when water is 0.24m from the top.
Fact
Idea
Learning Issue
Action plan
1. Vertex of cone point downward.
2. It has 45⁰ at half of the cone.
3. Height of filled water is 0.36m.
1. Find all the given information
2. Eg: volume of cone, and rate of water sinking.
1. What rule to apply?
2. How to apply given information into the correct rule?
Q&A Maths S & Maths T paper 1 by Khoo Ee Sin.

SOLUTION :
Let the height of the water at time t be x:
Volume, V=πx, r=radius of the water surface
Tan 45⁰= therefore r=x
V=π
=π Given =-
= x =π =-π(0.36 x =-0.39x1m When x=0.12 =π (0.12 Therefore:-0.39x1=π (0.12 =-7.5x1Therefore the water sinking rate is -7.5x1m

QUESTION 3 : The radius of the sphere is r, the area of the sphere and it’s volume is π. If, when the r of the sphere is 21m, it is