Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fi - Mathematics

Sum

A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill a container at the rate of ₹ 40 per litre.

#### Solution

Height of the frustum (h) = 16 cm

Radius of the upper part (R) = 20 cm

Radius of the lower part (r) = 8 cm

Volume of the frustum

= 1/3 pi"h" ["R"^2 + "r"^2 + "Rr"] cu.units

= 1/3 xx 22/7 xx 16 [20^2 + 8^2 + 20 xx 8] cu.units

= 1/3 xx 22/7 xx 16 [400 + 64 + 160] cu.units

= (22 xx 16 xx 624)/(3 xx 7) "cm"^3

= (22 xx 16 xx 208)/7 "cm"^3

= 73216/7

= 10459.43 cm3

= 10459.43/1000 "litre"

= 10.45943 litre

= 10.459 litre

Cost of milk in the container = 10.459 × 40 = ₹ 418.36

Cost of the milk = ₹ 418.36

Concept: Volume of Frustum of a Cone
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