I have 2 hemispheres witha radius of 9m, on either side of a cylicnder with a height of 30m

Question

1) Find the volume, correct to 2 decimal places.

 

2) If all its lengths are scaled up by 4, what is the new volume?

 

3) If all its lengths are acted on by a scale factor of 0.5, what is the new volume?

Answer 1

If you 'move' the shapes around in your mind, that may help. 2 hemispheres is 1 entire sphere. What is the formula for the volume of a sphere? You are left with a cylinder of radius 9 and length 30. What is the formula for a cylinder? Add up the volumes of the sphere and cylinder and you will have the answer to part A. Use the same idea for part B, but multiply every dimension (radius and length) by 4 and recalculate. In part C, 'scale factor' means 'multiplied by'. So multiple each dimension by 0.5 and then recalculate the volume.