Midterm Smackdown - Geo Water Tower Question

The water tower shown has a cone on top, a cylinder in the middle, and a hemisphere on the bottom. These 3D shapes can be modeled by different two dimensional shapes. Which 2D shapes make up this water tower?

• Half Circle

• Cylinder

• Rectangle

• Hemisphere

• Triangle

• Cone

Tags

CCSS.1.G.A.2

The 2 dimensional figure shown can be used to model the water tower from question #1. C is the center of the hemisphere and D is the center of the cone.

What is the radius of the hemisphere?

• 40

• 20

• 9

• no way to tell

• 3053.6281

• 1526.8140

• 339.2920

• 169.6460

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Is the radius of the hemisphere (9 ft) the same radius used for the cylinder and the cone?

• Yes

• No

• 5089.3801

• 2544.6900

• 180

• 565.4867

Tags

CCSS.5.MD.C.5C

In order to find the volume of the cone, we must know the radius and the height. We know that the radius is 9, but we do not know the height. What could we use to determine the height?

• Pythagorean Theorem

• SOHCAHTOA

• We don't have to do anything, the height is 9

• Law of Sines

Tags

CCSS.HSG.SRT.C.8

Using SOHCAHTOA on right triangle FDE where the radius, FD = 9, find the height of the cone (ED).

• 5.7851

• 10.7258

• 7.5519

• 6.8944

Tags

CCSS.HSG.SRT.C.8

• 650.2597

• 537.5063

• 1921.7245

• 640.5748

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Finally! If we know each of the volumes below, what is the total volume of the water tower to the nearest cubic foot?

Cone = 640.5748

Cylinder = 5089.3800

Hemisphere = 1526.8140

• 7257

• 7256

• 7255

• 7258

Tags

CCSS.5.MD.C.5C