Question

# The surface areas of two similar cylinders are 6cm² and 54cm². i. Find the scale factor for the enlargement. ii. If the larger cylinder has height 12cm, how high is the smaller one? iii. What is the ratio of their volumes?

Answer

Ratio of their volumes is 27:1

- Q: What is the formula for the surface area of a cylinder? A: The formula for the surface area of a cylinder is 2πr(r+h), where r is the radius and h is the height.
- Q: We are given that the surface areas of two similar cylinders are 6cm² and 54cm², therefore what can we say about their ratio? A: Since they are similar cylinders, the ratio of their surface areas is equal to the square of the scale factor.
- Q: What is the formula for the ratio of scale factor? A: The formula for the ratio of scale factor is the square root of the ratio of surface areas.
- Q: What is the square root of 54/6? A: The square root of 54/6 is 3, therefore the scale factor is 3.
- Q: If we know the scale factor, what formula can we use to find the height of the smaller cylinder? A: We can use the formula h₂ = h₁/scale factor, where h₁ is the height of the larger cylinder and h₂ is the height of the smaller cylinder.
- Q: What is 12/3? A: 12/3 is equal to 4, therefore the height of the smaller cylinder is 4cm.
- Q: What is the formula for the volume of a cylinder? A: The formula for the volume of a cylinder is πr²h.
- Q: What is the ratio of their volumes? A: Since the cylinders are similar, the ratio of their volumes is equal to the cube of the scale factor.
- Q: What is 3³? A: 3³ is equal to 27, therefore the ratio of their volumes is 27:1.