Volume and Area Problems

The volume of the larger cube is 5 cm^3 greater than the volume of the smaller cube. Show that . Find the volume of the smaller cube. Show all your working and give your answer correct to 2 decimal places.

The equation has one solution only when and when , where a and b are integers. Find the maximum value of a and the minimum value of b.

The difference between the areas of the two rectangles is 62 cm^2. Show that . Factorise . Solve the equation to find the difference between the perimeters of the two rectangles.

The probability that Andrei cycles to school is r. Write down, in terms of r, the probability that Andrei does not cycle to school.

The probability that Benoit does not cycle to school is . The probability that both Andrei and Benoit do not cycle to school is 0.4 . Complete the equation in terms of r. Show that this equation simplifies to . Solve by factorisation . Find the probability that Benoit does not cycle to school.

Find . Find . Find . Find in its simplest form. Find in the form . Find x when x = .

Factorise . The area of the rectangle is 84 cm^2. Find the perimeter.