A metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metalic sheet. The total vertical height of the bucket is 40 cm and that of cylindrical base is 10 cm, radii of two circular ends are 60 cm and 20 cm. Find the area of the metalic sheet used. Also find the volume of water the bucket can hold. (????= 3.14)
Answers
Dear Student,
Answer: Total sheet required = 3656.63 cm²
Total volume of water bucket = 163,362.82 cm³
Capacity of water bucket in litres = 163.36 ltr
Solution:
Total sheet required to manufacture bucket of given dimension:
Total surface area of frustum of cone + curved surface area of cylinder - area of top
∴ ( since bucket is open from top)
Refer attached diagram: area is to be calculated of coloured part only.
= π( r + R)h + πr² + πR² + 2π r h - πR²
∴ ( h for cone = 30 cm, h for cylinder = 10) cm
= π( r + R)h + πr² + 2π r h
= π ( rh + Rh + r² + 2rh)
= π ( 20 × 30 + 60 × 30 + 20² + 2 ×20 ×10)
= π( 600+1800+400+400)
Total sheet required = 3656.63 cm²
Volume of water bucket = volume of frustum of cone
( since base does not contained water)
Volume of water bucket = Volume of frustum of cone = 1/3 π × h (r² + rR + R²)
r = 20 cm
R = 60 cm
h = 30 cm
Volume of frustum of cone = 1/3 π × 30 ( 20² + 20(60) + 60²)
Volume of frustum of cone = 1/3 π × 30 ( 400+1200+3600)
= 10 π (5200)
= 52000 π
= 163,362.82 cm³
Total volume of water bucket = 163,362.82 cm³
Capacity of water bucket in litres = 163,362.82/1000 ltr
= 163.36 ltr
Hope it helps you.
Step-by-step explanation:
Please see the photo Hope it helps
