Question

38.
A bucket is in the form of a frustum of a cone of height 30 cm with radii of its
lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and
surface area of the bucket. Also find the cost of milk which can completely fill
the container at the rate of Rs. 25 per litre. (use t=3.14)
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Answer 1

Capacity of the bucket = 21.98 liters

Cost of the milk = ₹549.50

Surface area = 3292.87 cm²

Step-by-step explanation:

Capacity or volume of the frustum $\frac{\pi h}{3}[r_1^2+r_2^2+r_1\times r_2]$

Here,

π = 3.14

h = 30 cm

r₁ = 20 cm

r₂ = 10 cm

Now slant height of the frustum or bucket 'l' = $\sqrt{(r_{1}-r_{2})^{2}+h^{2}}$

l = $\sqrt{(20-10)^2+(30)^2}$

 = 10√10

 = 31.62 cm

Volume of the bucket = $3.14\times \frac{30}{3}[20^2+10^2+20\times 10]$

= $3.14\times \frac{30}{3}[400+100+20\times 10]$

= $31.4(700)$

= 21980 cm³

Converting cubic cm to liters

1 cubic cm = 0.01 liter

21980 cm³ = 21980 × 0.01 = 21.98 liters

Cost of 1 liter of milk = 25

Cost of 21.98 liters of milk = 25 × 21.98

                                           = ₹ 549.50

Surface area of the bucket

= Curved surface area + surface area of the bottom

=  $\pi (r_1+r_2)\times l+\pi \times (r_2)^2$

Here

$=3.14(20+10)\times 31.62+3.14\times 10^2$

= 3.14(30)(31.62) + 314

= 2978.87 + 314

= 3292.87 cm²

Capacity of the bucket = 21.98 liters

Cost of the milk = ₹549.50

Surface area = 3292.87 cm²

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