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.25 per litere . (Pie = 22/7).

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

The answer is incorrect :

Total surface area formula is used for finding the surface area while the bucket has no upper face.

Thus the formula used must be LSA of frustum + Lower Circle

The answer is 3290 cm^2