A wooden sphere 16 inches in diameter is placed on a table. The ball is cut horizontally 4in and 10in above the table surface. Find the surface area of the table remains after two cutting
not clear which part of the sphere is sitting on the table.
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To find the surface area of the table that remains after two horizontal cuts on the wooden sphere, we need to calculate the area of the circles created by each cut and subtract it from the total surface area of the sphere.
First, let's calculate the total surface area of the wooden sphere. The surface area of a sphere is given by the formula:
A = 4πr^2
Where A represents the surface area and r is the radius of the sphere.
Since we know the diameter of the sphere is 16 inches, we can find the radius by dividing the diameter by 2:
r = 16 inches / 2 = 8 inches
Now we can substitute the value of the radius into the formula to calculate the surface area:
A = 4π(8 inches)^2
= 4π(64 square inches)
= 256π square inches
The total surface area of the wooden sphere is 256π square inches.
Next, let's calculate the area of the circle created by the first cut, which is made 4 inches above the table surface. This circle will have a radius of 8 inches because it is the same as the radius of the sphere. We can use the formula for the area of a circle:
A = πr^2
Substituting the value of the radius, we get:
A = π(8 inches)^2
= π(64 square inches)
= 64π square inches
The area of the first circle is 64π square inches.
Similarly, let's calculate the area of the circle created by the second cut, which is made 10 inches above the table surface. This circle will have a radius of 8 inches as well. Using the same formula, we have:
A = π(8 inches)^2
= π(64 square inches)
= 64π square inches
The area of the second circle is also 64π square inches.
Now, let's subtract the areas of these two circles from the total surface area of the sphere to find the surface area of the table that remains:
Surface area of the table = Total surface area - Area of first circle - Area of second circle
= 256π square inches - 64π square inches - 64π square inches
= 128π square inches
So, the surface area of the table that remains after two horizontal cuts on the wooden sphere is 128π square inches.