Radius of larger cylinder (r₁) = 12 cm Height of larger cylinder (h₁) = 220 cm Radius of smaller cylinder (r₂) = 8 cm Height of smaller cylinder (h₂) = 60 cm Volume of pole = Volume of larger sylinder + Volume of smaller cylinder = πr₁ ²h₁ + πr₂² h₂ =π(12)² 220 + π(8)² × 60 = π[144 × 220 + 64 × 60]Read more
Radius of larger cylinder (r₁) = 12 cm
Height of larger cylinder (h₁) = 220 cm
Radius of smaller cylinder (r₂) = 8 cm
Height of smaller cylinder (h₂) = 60 cm
Volume of pole = Volume of larger sylinder + Volume of smaller cylinder
= πr₁ ²h₁ + πr₂² h₂
=π(12)² 220 + π(8)² × 60
= π[144 × 220 + 64 × 60] = 3.14 35520 = 111532.8 cm³
Mass of 1 cm³ of iron = 8 g
Therefore, the mass of 111532.8 cm³ of iron
= 111532.8 × 8 g = 892262.4g = 892.262 kg
Radius of hemispherical part = Radius of conical part = Radius of cylindrical part = 60 cm Height of cylindrical part (h1) = 180 cm, Height of conical part (h2) = 120 cm Volume of water left in the cylinder = Volume of cylinder - (Volume of hemisphere + Volume of cone) = πr²h₁ - (2/3πr³ + 1/3πr²h₂)Read more
Radius of hemispherical part = Radius of conical part = Radius of cylindrical part = 60 cm
Height of cylindrical part (h1) = 180 cm, Height of conical part (h2) = 120 cm
Volume of water left in the cylinder
= Volume of cylinder – (Volume of hemisphere + Volume of cone)
= πr²h₁ – (2/3πr³ + 1/3πr²h₂) = π(60)² × 180 -[(2/3)π(60)³ + 1/3π(60)² × 120]
= π (60)² [180 – (40 + 40)] = 22/7 × 60 × 60 × 100
= 1131428.57 cm³ = 1.131 m³
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8g mass.
Radius of larger cylinder (r₁) = 12 cm Height of larger cylinder (h₁) = 220 cm Radius of smaller cylinder (r₂) = 8 cm Height of smaller cylinder (h₂) = 60 cm Volume of pole = Volume of larger sylinder + Volume of smaller cylinder = πr₁ ²h₁ + πr₂² h₂ =π(12)² 220 + π(8)² × 60 = π[144 × 220 + 64 × 60]Read more
Radius of larger cylinder (r₁) = 12 cm
See lessHeight of larger cylinder (h₁) = 220 cm
Radius of smaller cylinder (r₂) = 8 cm
Height of smaller cylinder (h₂) = 60 cm
Volume of pole = Volume of larger sylinder + Volume of smaller cylinder
= πr₁ ²h₁ + πr₂² h₂
=π(12)² 220 + π(8)² × 60
= π[144 × 220 + 64 × 60] = 3.14 35520 = 111532.8 cm³
Mass of 1 cm³ of iron = 8 g
Therefore, the mass of 111532.8 cm³ of iron
= 111532.8 × 8 g = 892262.4g = 892.262 kg
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Radius of hemispherical part = Radius of conical part = Radius of cylindrical part = 60 cm Height of cylindrical part (h1) = 180 cm, Height of conical part (h2) = 120 cm Volume of water left in the cylinder = Volume of cylinder - (Volume of hemisphere + Volume of cone) = πr²h₁ - (2/3πr³ + 1/3πr²h₂)Read more
Radius of hemispherical part = Radius of conical part = Radius of cylindrical part = 60 cm
See lessHeight of cylindrical part (h1) = 180 cm, Height of conical part (h2) = 120 cm
Volume of water left in the cylinder
= Volume of cylinder – (Volume of hemisphere + Volume of cone)
= πr²h₁ – (2/3πr³ + 1/3πr²h₂) = π(60)² × 180 -[(2/3)π(60)³ + 1/3π(60)² × 120]
= π (60)² [180 – (40 + 40)] = 22/7 × 60 × 60 × 100
= 1131428.57 cm³ = 1.131 m³