Question

A container is in the form of frustum of a cone of height 30 cm with the radii of it's lower and upper ends as 10cm and 20cm respectively. Find the capacity and surface area of the container. Also find the cost of milk which can completely fill the container at the rate of ₹25per litre. Take,pie=3.14

Answer 1

Solution:-

Radius of the upper end of the frustum of cone = R = 20 cm
radius of the lower end of the frustum of cone = r = 10 cm
H = 30 cm
Volume = 1/3πh[R² + r² + R*r]
= 1/3*22/7*30*[20² + 10² + 20*10]
= 660/21*[400 + 100 + 200]
= (660*700)/21
= 22000 cu cm  or capacity = 22 liters
Now, Slant height 'l' = √(R - r)² + h²
l = √(20 - 10)² + 30²
l = √10² + 30²
l = √1000
l = 31.62 cm
Slant height is 31.62 cm
Surface area = πR² + πr² + π(R + r)l
= π[R² + r² + (R + r)*l]
= 22/7*[20² + 10² + (20 + 10)*30]
= 22/7*[400 + 100 + 30*30]
= (22*1400)/7
Surface area = 4400 sq cm
Cost of 1 liter milk = Rs. 25 
Total cost of 22 liter milk = 22*25
= Rs. 550
Answer.

Answer 2

Answer:

Surface area of bucket= 3292.6 cm² (approx.)

Cost of milk= Rs 549.50

Step-by-step explanation:

Capacity (or volume) of the container = [r21 + r22 + r1r2]

Here, h = 30 cm, r1 = 20 cm and r2 = 10 cm

So, the capacity of container = 3.14 x[202 + 102 + 20 x 10] cm3

= 21.980 liters

Cost of 1 litre of milk = Rs. 25

Cost of 21.980 litres of milk = Rs. 21.980 x 25 = Rs. 549.50

Surface area of the bucket = curved surface area of the bucket + surface area of the bottom

= l(r1 + r2) +r22

Now, l=  

l =cm = 31.62 cm

Therefore, surface area of the bucket

= 3.14 x 31.62 (20 + 10) + 3.14 x (10)2

= 3.14 x 1048.6 cm² = 3292.6 cm ² (approx.)