Using the formula for the surface area of a SPHERE:
Use Pi = 3.14
If the diameter of a sphere is 8 feet, find the surface area (round to the nearest square foot)
201 sq ft
If a quart of paint covers 75 square feet, how many quarts of paint are needed to paint the surface? quarts
What is the volume of the sphere? (round to the nearest cubic foot)
268 cubic ft
Using the rounded answer from the previous question, how many gallons of water can be stored in the sphere if 1 gallon= 231 cubic inches? (round this answer to the nearest TENTH of a gallon!)
are the two correct that i have done and how do i find the other two
radius of sphere = 4 feet
surface area of sphere = 4pir^2
= 4pi(16) = 200.96 feet^2 or 201 feet^2
so your first part is correct.
201/75 = 2.67 quarts
so you will have to buy 3 quarts
your volume answer is correct.
I trust that your statement
1 gallon = 231 cubic inches is correct, since I don't use those old units.
1 cubic foot = 12^3 cu inches = 1728 cubic inches.
so the 268 cubic feet from your answer equal 268*1728 or 463104 cubic inches.
463104/231 = 2005
there would be 2005 gallons of water
To find the surface area of a sphere, you can use the formula:
Surface Area = 4 * π * radius^2
Given the diameter of the sphere as 8 feet, you can find the radius by dividing the diameter by 2:
Radius = 8 feet / 2 = 4 feet
Now you can substitute the radius value into the formula to find the surface area:
Surface Area = 4 * 3.14 * (4 feet)^2
Surface Area = 4 * 3.14 * 16 square feet
Surface Area ≈ 201 square feet (rounding to the nearest square foot)
So, you have correctly found the surface area as 201 square feet.
To find the number of quarts of paint needed to paint the entire surface area of the sphere, you can divide the surface area by the coverage of paint per square foot.
Quarts of Paint Needed = Surface Area / Coverage of Paint per Square Foot
Given that a quart of paint covers 75 square feet, you can now calculate the quarts of paint needed:
Quarts of Paint Needed = 201 square feet / 75 square feet
Quarts of Paint Needed ≈ 2.68 quarts (rounding to the nearest quart)
So, you would need approximately 2.68 quarts of paint to paint the surface of the sphere.
To find the volume of the sphere, you can use the formula:
Volume = (4/3) * π * radius^3
Using the radius of the sphere as 4 feet, you can substitute it into the formula:
Volume = (4/3) * 3.14 * (4 feet)^3
Volume = (4/3) * 3.14 * 64 cubic feet
Volume ≈ 268 cubic feet (rounding to the nearest cubic foot)
So, the volume of the sphere is approximately 268 cubic feet.
To find the number of gallons of water that can be stored in the sphere, you need to convert the volume from cubic feet to cubic inches and then divide it by the conversion factor between gallons and cubic inches.
Volume in Cubic Inches = Volume in Cubic Feet * 12^3 (since 1 foot = 12 inches)
Volume in Cubic Inches = 268 cubic feet * (12 inches)^3
Volume in Cubic Inches = 268 cubic feet * 1728 cubic inches
Volume in Cubic Inches ≈ 462,336 cubic inches
Now, you can use the conversion factor to find the number of gallons:
Gallons of Water = Volume in Cubic Inches / 231 cubic inches (per gallon)
Gallons of Water = 462,336 cubic inches / 231 cubic inches
Gallons of Water ≈ 1,999.3 gallons (rounding to the nearest tenth of a gallon)
So, you can store approximately 1,999.3 gallons of water in the sphere.