1 ) Water flows at the rate of 10 metres/minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm.2 ) A circus tent has cylindrical shape surrounde by a conical roof. Base radius of the cylinder is 7 cm and height of the cylinder and cone are 6cm and 3cm respectively. Find the surface area of the tent.3 ) A tank 15m long, 10m wide, and 6m deep is open at the top. If the width of the sheet is 2m, then the cost of the iron sheet at the rate of Rs.5/m is

Dear Nithin,

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm

Speed of water = 10 m/min = 1000 cm/min

Volume of water that flows in 1 minute = Π r² h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm³

Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm

Therefore, Capacity of the vessel = 1/3 x Π r² h

= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm³

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

Best Of luck

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3 ) A tank 15m long, 10m wide, and 6m deep is open at the top. If the width of the sheet is 2m, then the cost of the iron sheet at the rate of Rs.5/m is

Let the radius of cylindrical pipe be r.Suppose the radius and height of the conical vessel be R and H respectively.Given: 2r = 5 mm 2R = 40 cm∴ R = 20 cmand H = 24 cmVolume of conical vessel Rate of water flow = 10 m/min = 1000 cm/min∴ Volume of water flowing out of the pipe in one minute = πr 2 � 1000 cm Let the time taken to fill the conical vessel be t minutes.∴ Volume of water flowing out of the pipe in t minutes Volume of water flowing out of the pipe in t minutes = Volume of conical vessel Thus, the time taken to fill the conical vessel is 51.2 minutes.