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A building is in the form of a cylinder surmounted by a hemisphere valted dome andcontains 41 m3 of air. If the internal diameter of dome is equal to its total heightabove the floor, find the height of the building.21 |
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Answer» Please like the solution 👍 ✔️👍 Let r be the radius of hemisphere & Cylinder and h be the height of the Cylinder, H be the height of the Total building.GIVEN :Volume of air = 880/21 m³Internal diameter (d) = HInternal Diameter = 2r = HTotal Height of the building (H) = 2r……(1)Height of the building = height of the cylinder + radius of the hemispherical DomeH = h + r 2r = h +r [from eq 1]2r -r = hr = h ……………..(2)Volume of air inside the building = Volume of cylindrical portion + Volume of hemispherical portionπr²h + (2πr³/3)= 880/21π(h)²h + (2π(h)³/3)= 880/21[From eq 2, r= h]πh³ + ⅔ πh³ = 880/21πh³(1+⅔) = 880/21πh³[(3+2)/3] = 880/21πh³[5/3] = 880/2122/7 × h³ × 5/3 = 880/21h³ = (880 ×3 ×7) / 21 × 22 × 5h³ = 40 /5 = 8h³ = 8h = ³√8 = ³√2×2×2h = 2 mh= r = 2 m [From eq 2, r= h]Total height of the building( H) = 2r = 2×2 = 4 mHence, the Total height of the building is 4m. HOPE THIS WILL HELP YOU… |
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