IGCSE Math Question

Question

1. Find the volume of a cylinder of radius 5cm and height 8cm. Give the units of your answer.
2. A ball falls d metres in t seconds. d is directly proportional to the square of t. The ball falls 44.1m in 3 seconds. a) Find a formula for d in terms of t. b) Calculate the distance the ball falls in 2 seconds.
3. P is the point (16, 9) and Q is the point (22, 24). (a) Find the equation of the line perpendicular to PQ that passes through the point (5, 1). Give your answer in the form y = mx+c. b) N is the point on PQ such that PN = 2NQ. Find the co-ordinates of N.

Please help me solve these questions step by step. Video is ok. Thanks so much

Answer 1

The formula for the volume of a right circular cylinder is V = πr²h. Substitute the given value for r and h and simplify. If you leave π in the answer you will have an exact value. If you substitute for π (3.1416 or 22/7) you will have an approximate answer. cm²cm means the final units will be cm³.

Directly proportional means both variables head in the same direction, both up or both down. If x and y are directly proportional than x = ky where k is a constant. d = kt². Substitute the given values for d and t to determine k. Now you have d = val t². Use that equation to determine d when t = 2. To find out more about directly proportional do a Google search.

For the 3rd question visit the graph with pencil and paper in hand, take some notes, then try to come up with the solution on your own.

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