A bucket is 32cm in diameter at the top and 20cm in diameter at the bottom. Find the capacity of the bucket in liter if is 21cm deep
Answers
The bucket is extended to form a cone (*See attachment)
AE is an extension of AC and BE is an extension of BD
⇒ Cone ABE is similar to Cone CDE
Using the property of similar figure.
AB/CD = EG/FE
32/20 = (21 + x)/x
32x = 20(21 + x)
32x = 420 + 20x
12x = 420
x = 35 cm
Height of the cone CDE = x cm = 35 cm
Height of the cone ABE = 21 + x = 21 + 35 = 56 cm
Radius of the cone ABE = Diameter ÷ 2 = 32 ÷ 2 = 16 cm
Radius of the cone CDE = Diameter ÷ 2 = 20 ÷ 2 = 10 cm
Find the volume of cone ABE:
Volume = πr²h
= π(16)²(56)
= 14336π cm³
Find the volume of cone CDE:
Volume = πr²h
= π(10)²(35)
= 3500π cm³
Find the volume of the bucket ABCD:
Volume = Volume of Cone ABE - Volume of Cone CDE
= 14336π - 3500π
= 10836π
= 34056 cm³
Answer: The volume of the bucket is 34056 cm³
