a solid wooden cylinder is to be cut from a solid block of wood. calculate the exact total surface area of the longest cylinder that can be cut out from a solid cube of side length 12 cm.
Question
a solid wooden cylinder is to be cut from a solid block of wood. calculate the exact total surface area of the longest cylinder that can be cut out from a solid cube of side length 12 cm.
Solution
The longest cylinder that can be cut out from a cube is a cylinder whose height is equal to the side length of the cube and whose diameter is equal to the side length of the cube.
The total surface area of a cylinder is given by the formula 2πr(h + r), where r is the radius and h is the height.
In this case, the side length of the cube is 12 cm, so the height of the cylinder, h, is also 12 cm. The diameter of the cylinder is also 12 cm, so the radius, r, is 12/2 = 6 cm.
Substituting these values into the formula gives:
Total surface area = 2π * 6 cm * (12 cm + 6 cm) = 2π * 6 cm * 18 cm = 216π cm².
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