You are chosen to represent the school in a Math Critical Thinkers Quest in your division. In order to win in the competition, you have to make a word problem depending on the topic given to you and make a step-by-step solution to the problem. Now, create your own word problem and provide solution for the problem in a clear and logical manner.
Answers & Comments
Topic: Variation
Problem:
The volume of a globe varies as the cube of its radius. Three solid globes of diameters 11/2, 2 and 21/2 metres are melted and formed into a new solid globe. Find the diameter of the new globe.
Solution:
STEP1:
Let V be the volume of a globe of radius R.
Then, by problem,
V ∝ R3
Therefore V = kR3 (1) [k = constant of variation ]
STEP2
If v1, v2 and v3 cubic metres be the respective volumes of globes having radii ¾, 1 and 5/4 metres then using (1) we get,
v1 = k × (3/4)3 = 27k/64 ;
v2 = k × l3 = k;
v3 = k × (5/4)3 = 125k/64
STEP3
Let v cubic metre be the volume of the new solid globe. Then,
v = v1 + v2 + v3 or, v = 27k/64 + k + 125k/64
or, v = 216k/64
or, v = 27k/8
STEP4
If the radius of the new solid globe be r metre, then using (1) we get,
v = kr3
or, kr3 = 27k/8
or, r3 = (3/2)3
or, r = 3/2.
Therefore, the diameter of the new globe =
2r = 2 × 3/2 = 3 metres.