Last updated at Feb. 25, 2017 by Teachoo
Example 9 Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use π= 3.14) Lets first find volume of water left in sump Volume of water left in the cuboidal sump after filling the tank = Volume of cuboidal sump – Volume of cylindrical tank Volume of cuboidal sump Length (l) = 1.57 m Breadth (b) = 1.44 m Height (h) = 95 cm = 95 ×1/100 m = 0.95 m Volume of sump = Length × Breadth × Height = lbh = 1.57 ×1.44 ×95 = 2.147 m3 Volume of overhead tank Height of overhead tank = h = 95 cm = 95×1/100 m = 0.95 m And, radius = r = 60 cm= 60×1/100 m = 0.6 m Volume of overhead tank = 𝜋𝑟2ℎ = 𝜋×(0.6)2×(0.95) = 0.342𝜋 m3 = 0.342×3.14 = 1.074 m3 Volume of water left in the cuboidal sump after filling the tank = Volume of cuboidal sump – Volume of cylindrical tank = 2.147 – 1.073 = 1.073 m3 Now, Volume of water left in cuboidal sump = 1.073 Length × Breadth × Height = 1.73 1.57 ×1.44 × h = 1.073 h = 1.073/(1.57 × 1.44) h = 0.475 m h = 0.475 × 100 cm h = 47.5 cm So, height of water left in sump = 47.5 cm Also, (𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡𝑎𝑛𝑘)/(𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑢𝑚𝑝) = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡𝑎𝑛𝑘)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑢𝑚𝑝) = 1.073/2.147 = 0.499 = 0.5 (approximately) = 5/10 = 1/2 Hence, capacity of the tank is half the capacity of the sump .
About the Author