A cylindrical tank has a height of 8 feet and a diameter of 2 3/4 feet.
Use pi= 3.14
What is the lateral surface area? square feet
What is the lateral surface area ? square inches
If a quart of paint covers 100 square feet, how many quarts of paint will be needed to paint the lateral surface area of the tank? quart(s) (Round to the nearest whole quart)
To find the lateral surface area of a cylindrical tank, we need to calculate the curved surface area of the cylinder.
The formula for the curved surface area of a cylinder is given by:
Curved Surface Area = 2πrh
Where:
π (pi) = 3.14 (given)
r = radius of the cylinder (half the diameter)
h = height of the cylinder
1. Radius:
The diameter of the cylinder is given as 2 3/4 feet. We need to convert it to inches and then divide by 2 to find the radius.
2 3/4 feet = 2.75 feet
2.75 feet * 12 inches/foot = 33 inches
Radius = 33 inches / 2 = 16.5 inches
2. Curved Surface Area:
Curved Surface Area = 2πrh
Substituting the given values:
Curved Surface Area = 2 * 3.14 * 16.5 inches * 8 feet
Now, we need to convert the result to square feet and square inches.
3. Convert to Square Feet:
1 foot = 12 inches
1 square foot = 12 inches * 12 inches = 144 square inches
Curved Surface Area in square feet = (Curved Surface Area in square inches) / 144
4. Convert to Square Inches:
Curved Surface Area in square inches = 2 * 3.14 * 16.5 inches * 8 feet
5. Quarts of Paint:
If a quart of paint covers 100 square feet, we can calculate the number of quarts needed by dividing the curved surface area by 100 and rounding to the nearest whole quart.
Now, let's calculate each step:
1. Radius = 16.5 inches
2. Curved Surface Area in square inches = 2 * 3.14 * 16.5 inches * 8 feet
3. Curved Surface Area in square feet = (Curved Surface Area in square inches) / 144
4. Quarts of Paint = (Curved Surface Area in square feet) / 100 (rounded to the nearest whole quart)
To find the lateral surface area of a cylindrical tank, we can use the formula:
Lateral Surface Area = 2πrh
Where:
- π is the mathematical constant pi, approximately equal to 3.14.
- r is the radius of the cylindrical tank, which can be found by dividing the diameter by 2.
- h is the height of the cylindrical tank.
Now, let's calculate the lateral surface area of the given cylindrical tank:
1. Calculate the radius:
The diameter of the tank is 2 3/4 feet. To find the radius, we divide this diameter by 2:
2 3/4 ÷ 2 = 11/4 ÷ 2 = 11/8 = 1 3/8 feet
2. Plug in the values into the formula:
Lateral Surface Area = 2 * 3.14 * (1 3/8) * 8
3. Simplify the expression:
Lateral Surface Area = 2 * 3.14 * (11/8) * 8
Lateral Surface Area = 2 * 3.14 * 11
4. Calculate the value:
Lateral Surface Area = 69.08 square feet (rounded to two decimal places)
Therefore, the lateral surface area of the cylindrical tank is approximately 69.08 square feet.
To find the lateral surface area in square inches, we need to convert square feet to square inches since there are 12 inches in a foot:
1 square foot = 12 * 12 = 144 square inches
Multiply the lateral surface area in square feet by 144 to convert it to square inches:
Lateral Surface Area in square inches = 69.08 * 144 = 9955.52 square inches (rounded to two decimal places)
Therefore, the lateral surface area of the cylindrical tank is approximately 9955.52 square inches.
For the next question, if a quart of paint covers 100 square feet, we can calculate the number of quarts needed to paint the lateral surface area:
Number of Quarts needed = Lateral Surface Area (in square feet) / Coverage per quart
Using the calculated lateral surface area of 69.08 square feet:
Number of Quarts needed = 69.08 / 100
Number of Quarts needed = 0.6908 quarts (rounded to four decimal places)
Rounded to the nearest whole quart, the number of quarts needed would be 1 quart.
Therefore, approximately 1 quart of paint will be needed to paint the lateral surface area of the tank.