the largest sphere is carved out of side 7 cm.find the volume of the sphere
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1. If it is carved out like that, the diameter of the sphere will be equal to the side of the cube. So diameter of the sphere is 7 cm, hence radius is 3.5 cm. So volume becomes (4/3).pi.r^3 = 539/3 = 179.667 cubic cm.
2. V of the cube in the prev. qstn. = 7^3 = 343 cubic cm. So ratio can be simply substituted by 343:539/3 = 21:11.
Otherwise, take side of cube as say 'a'. Then diameter of sphere being a, radius becomes a/2. Use the same result as above by substituting a^3: (4/3).pi.(a/2)^3 to get the same 21:11.
3. We know that volume of cone = (1/3)pi.h.r^2 and for cylinder pi.h.r^2. Clearly a cylinder has thrice the volume of the cone, hence when all the water in the cone is poured into the cylinder the height in the cylinder to which it rises will be 1/3rd the height of the cone, that is h/3.
2. V of the cube in the prev. qstn. = 7^3 = 343 cubic cm. So ratio can be simply substituted by 343:539/3 = 21:11.
Otherwise, take side of cube as say 'a'. Then diameter of sphere being a, radius becomes a/2. Use the same result as above by substituting a^3: (4/3).pi.(a/2)^3 to get the same 21:11.
3. We know that volume of cone = (1/3)pi.h.r^2 and for cylinder pi.h.r^2. Clearly a cylinder has thrice the volume of the cone, hence when all the water in the cone is poured into the cylinder the height in the cylinder to which it rises will be 1/3rd the height of the cone, that is h/3.
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