REVIEW : GEOMETRY

Find the area of a triangle with base of 6 m and altitude of 4 m.

12

Diameter of axle = 6" Axis of handle = 20" Weight lifted = 400 lb. How much force must be applied to the handle to lift the weight? Force =

120.0 lbs

Perform the following area application. Compute the square footage of carpet needed to cover a room 10' 6" × 12' 3".

128.6 sq ft

In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Speed of drive shaft = 825 r.p.m. Transmission in second gear Speed of engine =

1320 rpm

You are paneling an office that has 2 walls measuring 18' × 8' and 2 walls measuring 9' × 8'. How many sheets of paneling will you need, assuming each panel sheet measures 4' × 8'?

14 panels

peed of pulley A = 300 r.p.m. Speed of pulley B = Speed of pulley C = Speed of pulley D =

150 150 30

Find the surface area of a cube with sides of 5.5 cm each.

181.5 cm2

Volume of a pyramid: V = 1/3(area of base) × (altitude). A pyramid has an altitude of 4.7 in. and its base is a square with sides of 3.5 in. Find the pyramid's volume.

19.2 in3

Find the surface area of the following solid figure. A = r s. A cone's slant height is 14 cm and its radius is 4.5 cm.

197.8 cm2

Answer the following automotive services questions. Voltage = 12 v Current = 0.6 amps Resistance =

20 ohms

Find the surface area of the following solid figure. A = 4r 2. A sphere has a radius of 4 inches. Area (to the nearest tenth) =

201.0 sq in

Main drive gear = 35 teeth Speed of main drive gear = 450 r.p.m. Countershaft drive gear = 70 teeth Speed of countershaft drive gear =

225 rpm

Find the volume of the following solid figure. A cylinder has a radius of 2 feet and a height of 18 feet.

226.1 cu ft

Find the volume of the following solid figure. V = 1/3 r 2 h. A cone has a base with radius 5 inches. Its altitude is 9 inches.

235.5 cu in

Find the volume of the following solid figure. V = 4/3r 3. A sphere has a radius of 4 inches.

267.9 cu in

Find the volume of a cube whose sides each measure 3.2 cm.

32.8 cm3

Surface area of a pyramid: A = 1/2(perimeter of base) × (slant height) + (area of base). A pyramid has a base measuring 3 meters × 3 meters. Its slant height is 5.5 meters. Find the surface area of the pyramid.

42.0 m2

Find the area of a trapezoid whose parallel sides measure 8.5 m and 4.5 m, and whose altitude is 6.5 m. To the nearest tenth, area = m 2.

42.25 m2

In this fulcrum, for the weights to be in balance, what do the distances d1 and d2 have to be if the overall length is 12 feet? d1 (to the nearest hundredth) = d2 (to the nearest hundredth)

5.45 6.55

A rectangular solid has sides of 10 cm, 6.5 cm, and 8.3 cm. What is its volume?

539.5 cm3

A cylinder has an elliptical base with major semiaxis length of 6 cm and minor semiaxis length of 4 cm. Its altitude is 7.5 cm. Find the volume of the cylinder. (Hint: Volume of the cylinder = area. of base × altitude.) Volume (to the nearest tenth) =

565.2 cm 3.

Current = 0.11 amps Resistance = 55 ohm Voltage

6.05 volts

You decide to build a pyramid in your back yard. If the pyramid is to have a slant height of 8 ft. and its perimeter is to be a perfect square measuring 4 ft. on each side, what will the total surface area of the pyramid be? A = 1/2(perimeter of base) × (slant height) Surface area (to the nearest tenth) =

64 sq ft

You have constructed wooden forms for pilings. The pilings are in the shape of rectangular solids, each measuring 20 ft. high and 2 ft. square. You are now going to pour cement into 10 of these forms. How much cement will you pour?

800 cu ft

Speed of pulley D = 125 r.p.m. Note: diameter of pulley C = 1.5" Speed of pulley A (to the nearest r.p.m.) =

833 rpm

Find the areas of the following geometric figure. An ellipse has a major semiaxis of 20 cm and a minor semiaxis of 14 cm.

879.2cm2

Solve the following solid figure application problem. How many liters of paint are contained in a can measuring 8.5 inches across its base and 10 inches high. Hint: 1 inch = 2.54 cm; 1 liter = 1000 cm 3

9.29 l

In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 2,700 r.p.m. Transmission in first gear Speed of shaft =

900 rpm

Given a rectangular solid 3 in. × 4 in. × 5 in., what is its surface area?

94.0 sq in

Find the missing value. A can of oil has a surface area of 225 cm 2. If the can is 9.5 cm high, what is the diameter across its base?

diameter : 7.5 cm