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Full solution please and use integration

A cylindrical container, without a lid, is held in such a way that its axis makes an angle of pi / 6 radians with a horizontal plane. Suppose the diameter of the cylinder is 4 and that its heig

User Izumi
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Final answer:

To find the inside radius of the coffee mug, we can use the formula for the volume of a cylinder and solve for the radius. By substituting the known values into the formula, we can find that the inside radius is approximately 2.24 cm.

Step-by-step explanation:

To find the inside radius of the coffee mug, we need to consider the volume of the coffee it holds. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. In this case, we know that the coffee weighs 375 g and has a density equal to that of water. Since the density of water is 1 g/cm³, the volume of the coffee can be calculated by dividing the weight by the density: V = 375 g / 1 g/cm³ = 375 cm³. The height of the coffee in the mug is given as 7.50 cm. Substituting these values into the formula, we can solve for the inside radius:

375 cm³ = πr²(7.50 cm)

Dividing both sides of the equation by π(7.50 cm), we get:

r² = 375 cm³ / (π(7.50 cm))

r² = 5 cm

Taking the square root of both sides, we find:

r ≈ 2.24 cm

User Matt Fortier
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