Assignment:
Q1. A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.
S=_______
Q2. The diameter of a spherical balloon is 8 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
Note the volume of a sphere with radius R is V=4/3(π)R^3
The increase in volume is equal to _____________ cm^3
Q3. A rectangle has its base lying on the x axis and its upper corners on the parabola y=8 - x^2. If the upper right corner is (s,t), express the area A of the rectangle as a function of s.
The area of the rectangle is A=________
Provide complete and step by step solution for the question and show calculations and use formulas.