A cylindrical tank if 8 ft. in diameter and 20 ft tall. how many gallons of paint are needed to paint the tank if one gallon covers 200 sq ft ?

and

a cylindrical hole with diameter 8 inches is cut through a cube 10 in. on a side. find the surface area of this solid

HOW PLEASE. huhu please help. just tell me how pleaaaase.

the area is 2πr(r+h)

since 1 gallon covers 200ft^2, just divide the area by 200
Note r=4,h=20
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Assuming the axis of the cylinder is parallel to an edge of the cube, what you have is just a cylinder where r=4 and h=10

area is figured as above, so the answer is 1/2 the value obtained above.

To find the number of gallons of paint needed to paint the cylindrical tank, follow these steps:

Step 1: Calculate the surface area of the tank's curved side.
The formula for the surface area of a cylinder's curved side is A = 2πrh, where A is the surface area, π is approximately 3.14, r is the radius of the cylinder, and h is the height.

Given:
Diameter = 8 ft
Radius (r) = 8 ft / 2 = 4 ft
Height (h) = 20 ft

A = 2πrh = 2 * 3.14 * 4 ft * 20 ft = 502.4 sq ft

Step 2: Calculate the total surface area of the tank.
The tank has a top and bottom that also need to be painted.
The formula for the surface area of a circle is A = πr^2.

Top and bottom surface area = 2 * π * (radius)^2 = 2 * 3.14 * (4 ft)^2 = 100.48 sq ft

Total surface area of the tank = Surface area of curved side + Top and bottom surface area
Total surface area = 502.4 sq ft + 100.48 sq ft = 602.88 sq ft

Step 3: Calculate the number of gallons needed.
Given that one gallon of paint covers 200 sq ft, divide the total surface area by the coverage area of one gallon.

Number of gallons needed = Total surface area / Coverage area per gallon
Number of gallons needed = 602.88 sq ft / 200 sq ft/gallon = 3.0144 gallons

Therefore, you would need approximately 3 gallons of paint to paint the tank.

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To find the surface area of the solid created by cutting a cylindrical hole with an 8-inch diameter through a 10-inch cube, follow these steps:

Step 1: Calculate the surface area of the cube.
The surface area of a cube can be calculated using the formula A = 6s^2, where A is the surface area and s is the length of its side.

Given:
Side length (s) = 10 inches

Surface area of the cube = 6 * (10 in)^2 = 600 sq in

Step 2: Calculate the surface area of the cylindrical hole.
The formula for the surface area of a cylinder is A = 2πrh + πr^2, where A is the surface area, π is approximately 3.14, r is the radius of the cylinder, and h is the height.

Given:
Diameter = 8 inches
Radius (r) = 8 in / 2 = 4 inches

The cylindrical hole runs through the cube, so its height will be equal to the side length of the cube.

Height (h) = 10 inches

Surface area of the cylindrical hole = 2πrh + πr^2 = 2 * 3.14 * 4 in * 10 in + 3.14 * (4 in)^2
Surface area of the cylindrical hole = 251.2 sq in + 50.24 sq in = 301.44 sq in

Step 3: Calculate the surface area of the solid.
The surface area of the solid will be the surface area of the cube minus the surface area of the cylindrical hole.

Surface area of the solid = Surface area of the cube - Surface area of the cylindrical hole
Surface area of the solid = 600 sq in - 301.44 sq in = 298.56 sq in

Therefore, the surface area of the solid created by cutting a cylindrical hole with an 8-inch diameter through a 10-inch cube is approximately 298.56 square inches.

Sure! I'll be happy to help you solve these problems step by step.

To find the number of gallons of paint needed to paint the cylindrical tank, you need to calculate the surface area of the tank and then divide it by the coverage area of one gallon of paint.

1. Find the surface area of the tank:
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh,
where r is the radius, and h is the height of the cylinder.
Given that the diameter (d) of the tank is 8 ft, the radius (r) can be calculated by dividing the diameter by 2:
r = d/2 = 8 ft / 2 = 4 ft.
The height (h) of the tank is given as 20 ft, so we have:
Surface Area = 2π(4²) + 2π(4)(20) = 32π + 160π = 192π sq ft.

2. Find the number of gallons needed:
Since one gallon covers 200 sq ft, we can divide the surface area of the tank by 200 to get the number of gallons needed:
Number of gallons = Surface Area / Coverage per gallon = 192π / 200 ≈ 3.046π ≈ 9.58 gallons (rounded to two decimal places).

So, approximately 9.58 gallons of paint are needed to paint the tank.

Now, let's move to the second problem.

To find the surface area of the solid obtained by cutting the cylindrical hole through the cube, you need to calculate the surface area of the cube and subtract the area of the cylindrical hole.

1. Find the surface area of the cube:
The surface area of a cube can be calculated using the formula:
Surface Area = 6s²,
where s is the side length of the cube.
Given that the side length (s) is 10 in, we have:
Surface Area = 6(10²) = 600 sq in.

2. Find the area of the cylindrical hole:
The area (A) of a cylinder with diameter (d) and height (h) can be calculated using the formula:
A = 2πr² + πdh,
where r is the radius, and h is the height of the cylinder.
Given that the diameter (d) of the hole is 8 in, the radius (r) can be calculated by dividing the diameter by 2:
r = d/2 = 8 in / 2 = 4 in.
The height (h) of the hole is equal to the side length of the cube, which is 10 in, so we have:
A = 2π(4²) + π(4)(10) = 32π + 40π = 72π sq in.

3. Find the surface area of the solid:
Subtract the area of the hole from the surface area of the cube:
Surface Area = Cube Surface Area - Hole Area = 600 - 72π ≈ 379.35 sq in (rounded to two decimal places).

So, the surface area of the solid is approximately 379.35 sq in.

I hope this helps you understand how to solve these problems! Let me know if you have any more questions.