91影视

As 90% of the height of the block is submerged, the submerged volume can be calculated as the volume of a cone with 0.9h as its height. We know that the height and diameter of the block are equal to 20 cm, so we can write the ratio of the submerged volume to the total volume as: \[\frac{V_{sub}}{V_{total}} = \left(\frac{0.9h}{h}\right)^3 = 0.9^3\] Calculate the total volume of the complete cone using the formula \(V_{total} = \frac{1}{3}蟺r^2h\), where h is the height, and r is the radius of the cone.

From the previous step, we know that the height and diameter of the block are equal to 20 cm. Therefore, the radius at the base of the cone is half of 20 cm, which is 10 cm. Now calculate the total volume of the block using the formula for the volume of a cone: \[V_{total} = \frac{1}{3}蟺r^2h = \frac{1}{3}蟺(10)^2(20)\] Now we can find the volume of the submerged portion, \(V_{sub}\), by multiplying the total volume by the ratio we found in step 1: \[V_{sub} = V_{total} 脳 0.9^3\]

By the principle of buoyancy, we know that the buoyant force experienced by the block is equal to the weight of the displaced water. The volume of the displaced water is equal to the volume of the submerged portion, \(V_{sub}\). The weight of the displaced water (\(W_{water}\)) can be written as: \[W_{water} = m_{water} 脳 g\] Where \(m_{water}\) is the mass of the displaced water, and g is the acceleration due to gravity. We also know that the mass of the displaced water can be found using the formula: \[m_{water} = 蟻 脳 V_{sub}\] 蟻 is the density of water (蟻 = 1000 kg/m鲁), and \(V_{sub}\) is the submerged volume of the block. Now, we will find the total weight of the block (\(W_{block}\)): \[W_{block} = W_{water} - m 脳 g\] Where m is the mass to be kept on the block so that the block just floats at the surface of the water.

From step 3, we know the equation relating the total weight of the block to the weight of the displaced water. We can now solve for the additional mass m that needs to be added to the block: \[m = \frac{W_{water} - W_{block}}{g}\] Now, we can substitute the values of \(W_{water}\) and \(W_{block}\) into this equation and solve for m. After calculating the mass, compare the result with the given options: (A) \(568 \mathrm{~g}\) (B) \(980 \mathrm{~g}\) (C) \(112 \mathrm{~g}\) (D) \(196 \mathrm{~g}\) Choose the closest option.