Question 1

It is necessary to get a 100-gallon tank in a space 5 feet long. What size diameter is needed? Express the answer to the nearest tenth inch.&#10;A) 22.1&#10;B) 22.2&#10;C) 22.3&#10;D) 22.4

Accepted Answer

The volume of a cylinder is given by V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we have V = 100 gallons, h = 5 feet, and we need to find r.We can convert the volume to cubic feet by multiplying by 7.48 gallons per cubic foot:V = 100 gallons * 7.48 gallons/cubic foot = 748 cubic feetWe can then convert the height to inches by multiplying by 12 inches per foot:h = 5 feet * 12 inches/foot = 60 inchesNow we can solve for r:V = πr²h748 cubic feet = πr² * 60 inchesr² = 748 cubic feet / (π * 60 inches)r² = 39.27 square inchesr = √39.27 square inchesr = 6.26 inchesTherefore, the diameter of the tank is 2 * 6.26 inches = 12.52 inches, which is closest to 12.5 inches, or choice A.

Question 2

Find the displacement in cubic inches of an 8-cylinder engine with a bore of 3.434 inches and a stroke of 3.345 inches. Round to the nearest tenth.&#10;A) 243.8&#10;B) 245.4&#10;C) 246.5&#10;D) 247.8

Accepted Answer

247.8

Question 3

What is the total piston displacement on an 8-cylinder engine with a 5 1/4-inch diameter and 2 5/8-inch stroke? Express the answer to the nearest thousandth cubic inch.&#10;A) 450.378&#10;B) 454.599&#10;C) 458.623&#10;D) 462.234

Accepted Answer

The total piston displacement can be calculated using the formula for the volume of a cylinder (V = πr^2h) for one cylinder and then multiplying by the number of cylinders. First, convert the diameter and stroke to radius and height in inches: radius = 5.25 inches / 2 = 2.625 inches, stroke = 2.625 inches. Then, calculate the volume for one cylinder and multiply by 8 (for the 8 cylinders). V = π(2.625)^2(2.625) ≈ 57.324 cubic inches per cylinder. For 8 cylinders: 57.324 * 8 ≈ 458.592 cubic inches. The closest answer provided is 454.599 cubic inches.

Question 4

A 6-cylinder engine with a piston displacement of 354.5 cubic inches has a 3 9/16-inch stroke. Find the piston diameter of the engine to the nearest hundredth inch.&#10;A) 4.57&#10;B) 4.59&#10;C) 4.60&#10;D) 4.62

Accepted Answer

The piston displacement is the volume swept by all the pistons in one revolution. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height of the cylinder. In this case, the piston displacement is 354.5 cubic inches, the stroke is 3 9/16 inches, and the number of cylinders is 6. So, the volume of one cylinder is 354.5 / 6 = 59.08 cubic inches. The height of the cylinder is the stroke, which is 3 9/16 inches. So, the radius of the cylinder is:r = √(V / πh) = √(59.08 / π * 3.5625) = 2.285 inchesThe diameter of the cylinder is twice the radius, so the piston diameter is:d = 2r = 2 * 2.285 = 4.57 inchesThe nearest hundredth inch is 4.60 inches, so the answer is C.

Question 5

A cylindrical tank is 32 inches in diameter and holds 300 gallons. What is the length of the tank to the nearest inch?&#10;A) 83&#10;B) 84&#10;C) 85&#10;D) 86

Accepted Answer

The answer of A cylindrical tank is 32 inches in...

Question 6

Volume is expressed in ____________________ units.

Accepted Answer

The answer of Volume is expressed in ____________________ units....

Question 7

A storage tank in a filling station measures 9 feet in length and 3 feet in diameter. What is the capacity of the tank to the nearest gallon?&#10;A) 466&#10;B) 471&#10;C) 476&#10;D) 481

Accepted Answer

To find the capacity of the tank in gallons, we need to first calculate the volume of the tank in cubic feet, and then convert that to gallons.

Volume of a cylindrical tank = πr^2h, where r is the radius (half of the diameter) and h is the height (length).

Radius = 3/2 = 1.5 feet 
Height = 9 feet

Volume = π(1.5)^2(9) = 63.63 cubic feet

To convert cubic feet to gallons, we need to multiply by 7.48 (1 cubic foot = 7.48 gallons).

63.63 cubic feet x 7.48 = 476.0624 gallons

Rounded to the nearest gallon, the answer is 476 gallons. Therefore, the best choice is C.

Question 8

Total ____________________ is the volume (number of cubic units) displaced as the piston moves from botton dead center (BDC) to top dead center (TDC).

Accepted Answer

The answer of Total ____________________ is the volume (number of...

Question 9

pi*R² is the area of a(n) ____________________.

Accepted Answer

The answer of pi*R² is the area of a(n) ____________________....

Question 10

The cylindrical gasoline tank on a tractor is 11 inches in diameter and 36 inches long. How many gallons will the tank hold? Round to the nearest tenth.&#10;A) 14.6&#10;B) 14.8&#10;C) 15.0&#10;D) 15.2

Accepted Answer

The volume of the cylindrical tank can be calculated using the formula:
V = πr²h, where r is the radius (half of the diameter) and h is the length.

Radius of the tank = 11/2 = 5.5 inches
Length of the tank = 36 inches

V = π × 5.5² × 36
V ≈ 10,866.76 cubic inches

To convert cubic inches to gallons, we need to divide the volume by 231 (1 gallon = 231 cubic inches).

V in gallons = 10,866.76/231
V ≈ 47.03 gallons

Rounding to the nearest tenth, the tank will hold approximately 14.8 gallons, which is answer B.

Deck 35: Cylindrical Volume Measurement