Question

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 rete of Rs.40
per litere . (Pie = 22/7).

Answer 1

AnswEr:-

Volume of the Bucket = $\sf\dfrac{\pi rh}{3}$

$\sf\; r^2_1 + r^2_2 + r_1 r_2$

Given :-

• Height = 30 cm
• $\sf\; r_1 = 20 \;cm$
• $\sf\; r_2 = 10 \; cm$

So, the capacity of the bucket = $\sf\; 3.14 = \dfrac{30}{3}$

$:\implies\sf\; 20^2 + 10^2 + 20 \times\; 10\; cm^3$

$:\implies\sf\; 21980\; cm = 21.980 \; litres$

Now, According to Question :-

Cost of 1 litre of milk = 40 Rs.

Cost of 21980 litres of milk = Rs 21.980 × 40

Rs = 879.20

$\rule{150}2$

Surface area of the bucket :-

Curved surface area of the bucket + Surface area of the bottom

$:\implies\sf\; \pi(r_1 + r_2 ) + \pi \; r_2^2$

Where,

$:\implies\sf\; l = \sqrt{h^2 + (r_1 + r_2)}$

$:\implies\sf\; l = \sqrt{900 + 100\; cm}$

$:\implies\sf\; 31.62 cm$

$\rule{150}2$

Therefore, Surface area of the bucket =

$:\implies\sf\dfrac{22}{7}\times\; 31.62 (20 + 10) + \dfrac{22}{7} \times \; 10^2$

$:\implies\sf\; \dfrac{22}{7} \times 1048.6$

$:\implies\large\boxed{\sf{\red{3295.6 \;cm\;(approx)}}}$

$\rule{150}2$