Question

question 5: standard g.mg.1
a cone shape might best model which of the following?
a. coffee mug
b. bowl
c. ice cream cone
d. a trash can
question 6: standard g.mg.1
which shape has the smallest surface area for any given volume?
a. cone
b. cylinder
c. sphere
d. square based pyramid
for questions 7-9 use the following information.
image of a lamp
you want to find the volume of a lamp shade in your house. you measure the radius to be 10 inches and the height to be 4 inches.
question 7: standard g.mg
which shape should you model your lampshade after?
a. cylinder
b. sphere
c. square based pyramid
d. hexagonal pyramid
question 8: standard g.mg
which formula should you use to find the volume of the lamp shade?
a. $v = \pi r^2 h$
b. $v = (\pi r^2 h) / 3$
c. $v = (\text{area}_{\text{base}} h) / 3$
d. $v = (4/3)\pi r^3$

Explanation:

Question 5

A coffee mug is usually a cylinder, a bowl is more like a hemisphere or a shallow cylinder, a trash can is a cylinder. An ice cream cone has a conical shape (a cone with a flat circular base and a pointed top, but the main part is conical). So the cone shape best models an ice cream cone.

Among the given shapes (cone, cylinder, sphere, square - based pyramid), the sphere has the property that for a given volume, it has the smallest surface area. This is a well - known result in geometry related to the isoperimetric inequality for three - dimensional shapes.

A lampshade is typically a cylinder. A sphere is a round ball - like shape, a square - based pyramid has a square base and triangular sides, and a hexagonal pyramid has a hexagonal base and triangular sides. A lampshade has a circular (or approximately circular) base and a height, so it is modeled as a cylinder.

Answer:

c. Ice cream cone

Question 6