A right cylinder has a radius of 3 cm and a height of 5 cm. Answer the following questions and make sure to show all your work.

(a) Find the Surface Area of the cylinder.

(b) Find the Volume of the cylinder.

(c) If you wanted more volume in your cylinder, which of these two ideas would give the most Volume?

1. Doubling the radius to 6 cm, while the height remains 5 cm.

-OR-

2. Tripling the height to 15 cm, while the radius remains 3 cm.

Question 1 options:
Question 2 (5 points)

A scoop of ice cream in the shape of a whole sphere sits in a right cone. the radius of the ice cream scoop is 2.5 cm and the radius of the cone is 2.5 cm. How tall must the height of the cone be to fit all the ice cream without spilling if it melts? Show all your work.

Question 2 options:
Question 3 (5 points)

Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the larger. Only the smaller pyramid is shown.

She calculates the area of the base of the pyramid (through long, hard work) to be 110.11 square units. The height of the pyramid is 12 units. Now she needs to calculate the volume of the pyramid.

(a) Calculate the volume of the pyramid for Sarah.

(b) "Oh, no!" Sarah exclaims. "Now I have to go through all this hard work again to find the volume of the larger pyramid!" Does she? Explain.

(c) Calculate the volume of the larger pyramid for Sarah.

Question 3 options: