An open cylindrical vessel has a total surface area of 2002 square centimeters. If the radius of its base is 7 cm, how many liters of water can it hold? (1 liter = 1 cubic decimeter)

Q.An open cylindrical vessel has a total surface area of 2002 square centimeters. If the radius of its base is 7 cm, how many liters of water can it hold? (1 liter = 1 cubic decimeter)

Let the height of the vessel be \(h\) cm. The radius of the vessel \(r = \cfrac{14}{2} = 7\) cm. Therefore, the total surface area of the open cylindrical vessel is: \(\pi r^2 + 2\pi rh\) square cm \(= \pi r(r + 2h)\) square cm \(= \cfrac{22}{7} \times 7 \times (7 + 2h)\) square cm \(= 22(7 + 2h)\) square cm Given: \(22(7 + 2h) = 2002\) ⇒ \(7 + 2h = \cfrac{2002}{22} = 91\) ⇒ \(2h = 91 − 7 = 84\) ⇒ \(h = \cfrac{84}{2} = 42\) So, the height of the vessel \(h = 42\) cm = 4.2 decimeters And the radius \(r = 7\) cm = 0.7 decimeters Therefore, the volume of the vessel = \(\pi r^2 h\) cubic decimeters \(= \cfrac{22}{7} \times (0.7)^2 \times 4.2\) cubic decimeters \(= \cfrac{22}{7} \times \cfrac{7 \times 7}{100} \times \cfrac{42}{10}\) cubic decimeters \(= 6.468\) cubic decimeters = 6.468 liters [Since 1 cubic decimeter = 1 liter] ∴ The vessel can hold 6.468 liters of water.