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makes in 10 minutes when the ear is travelming at d spccu UI21.A hollow sphere of extemal and internal diameters 8 em and 4 cm respectively is melted into acone of base diameter 8 cm. Find the height of the conetuher tested in a tuhe comnany is |
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Answer» Given : Internal diameter of hollow sphere(d)= 4 cm.Internal radius of hollow sphere (r) = 4/2= 2 cmexternal diameter of hollow sphere (D) = 8 cm.external radius of hollow sphere( R )= 8/2= 4 cm. Volume of the Hollow sphere = 4/3π(R³ - r³)Volume of the Hollow sphere = 4/3π(4³ - 2³)Volume of the Hollow sphere = 4/3π(64 - 8)Volume of the Hollow sphere = 4/3π(56) cm³ Diameter of the cone(d1) = 8 cmradius of the cone( r1)= 8/2 = 4 cm Let the height of the cone be h cm.Volume of the cone = ⅓ πr1²h= ⅓ π × 4² × h = 16πh/3 Volume of the cone = Volume of the hollow sphere16πh/3 = 4/3π(56)16h = 4 ×56h = (4 × 56)/16h = 56/4 = 14 cm Hence, the height of the cone is 14 cm. |
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