Question 7
An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig. 13.23). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold.(Take = 22/7)
Area of metallic sheet used
= curved surface area of frustum
+ curved surface area of cylinder
+ area of circular base
Curved surface area of frustum
Diameter of bigger circular end = 45 cm
Radius = r1 = 45/2 cm
Diameter of smaller circular end = 25 cm
Radius = r2 = 25/2 cm
Now,
Height of frustum = Total height of bucket Height of cylinder
= 40 6 = 34 cm
Also,
Slant height of frustum (l) = (h2+(r1 r2)2)
= ((34)2+( 45/2 25/2)^2 )
= ((34)2+( (40 25)/2)^2 )
= ((34)2+(20/2)2)
= ((34)2+(10)2)
= (1156+10)
= 1256
= 35.44 cm
Curved surface area of frustum = (r1+r2)
= 35.44(45/2+25/2)
= 35.44 (70/2)
= 35.44 35
= 1240.4 cm2
Area of circular base
Base is a circle with radius = r2 = 25/2
Area of circular base = r22
= (25/2)^2
= (12.5)2
= 156.25 cm2
Curved Surface Area of cylinder
Radius of cylinder = r2 = 25/2
Height of cylinder = 6 cm
Curved Surface Area of cylinder = 2
= 2 25/2 6
= 150 cm2
Now,
Area of metallic sheet used
= curved surface area of frustum + area of circular base
+ curved surface area of cylinder
= 1240.4 +156.25 +150
= (1240.4+156.26+150)
= 22/7 (1546.66)
= 22 220.95
= 4860.9 cm2
Now,
We need to find volume of water in bucket
Volume of water in bucket = Volume of frustum
= 1/3 ( 12+ 22+ 2 2)
= 1/3 22/7 34 ((45/2)^2+(25/2)^2+45/2 25/2)
= 22/7 34/3 (( 22.5)2+(12.5)2+22.5 12.5)
= 22/7 34/3 (506.25 + 156.25 + 281.25)
= 22/7 34/3(943.75)
= 22 34 44.94
= 33615.48 cm3
= 33615.48/1000 litres
= 33.62 litres (approx.)
Hence, area of metallic shed used = 4860.9 cm2
Volume of water that bucket can hold = 33.62 litres (approx.)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!