Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below : The total height of the…
CBSE Class 10 Maths PYQ · Surface Areas & Volumes · Both · 5 Marks · March 2025 · Standard
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675 Marks · March 2025 · Standard
Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below : The total height of the tank is $3.3$ m and height of conical part is $1.2$ m. The diameter of the cylindrical as well as conical part is $1$ m. Find the capacity of the tank. If the level of liquid in the tank is $0.7$ m from the top, find the surface area of the tank in contact with liquid.
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Diameter $= 1$ m, $r = 0.5$ m. Height of Cylinder $(H) = 3.3 - 1.2 = 2.1$ m. Capacity of the tank = Volume of cylinder + Volume of cone $= \frac{22}{7} \times (0.5)^2 \times 2.1 + \frac{1}{3} \times \frac{22}{7} \times (0.5)^2 \times 1.2 = 1.96$ m$^3$. Slant height $(l) = \sqrt{(1.2)^2 + (0.5)^2} = 1.3$ m. Height of cylindrical part in contact with liquid $= 2.1 - 0.7 = 1.4$ m. Surface area of tank in contact with liquid = Curved Surface Area of Cylindrical part in contact with liquid + Curved surface Area of cone $= 2 \times \frac{22}{7} \times 0.5 \times 1.4 + \frac{22}{7} \times 0.5 \times 1.3 = 6.44$ m$^2$ (approx.)
