Sketch a cone with the vertex downwards , and top radius of 28 cm
create a truncated cone by sketching a cone inside this one with a top radius of 21
The top part of your diagram is your bucket.
The first part is to find the height of the bucket.
let the height of the bottom part of the cone, (the part we will cut off) be x
let the height of the bucket part be h
by ratios:
28/(x+h) = 21/x
21x + 21h = 28x
21h = 7x
x = 3h
So the whole cone has a height of x+h or 4h
and the bucket has a height of h
Volume of whole cone = (1/3)π (28^2)(4h)
volume of bottom part = (1/3)π (21^2)(h)
volume of bucket = difference between the above two expression, and factoring
= (1/3)π(h) (4(28^2) - 21^2)
= 2822.1974h
but the volume is given as 28.49 L = 28490 cm^3
so 2822.1974h = 28490
h = 10.09 cm
Now we need the lateral surface area + area of the bottom of the bucke
the last part would simply be 2π(21) or 42 π
the first part is harder:
look at
http://www.vitutor.com/geometry/solid/truncated_cone.html
and continue from there
There is also a lateral surface area of a truncated cone Calculator, (how about that ?)
enter 28 or top radius
enter 21 for bottom radius
enter 10.09 for height, (don't choose slant height)
to get 5738.87 cm^2
good luck
A bucket holds 28.49 liters of milk .the radii of the top and bottom are 28cm and 21 cm respectively.find the total surface area of the bucket.
8 answers
forgot to give you the link to the calculator
http://www.onlineconversion.com/object_surfacearea_trunc_cone.htm
http://www.onlineconversion.com/object_surfacearea_trunc_cone.htm
extend the cone of the bucket, so it is of height H. The height h of the bucket is H/4 since 21/28 = 3/4.
subtract the volume of the 21cm cone from a 28-cm cone:
v = 1/3 pi 28^2 H - 1/3 pi 21^2 h
pi/3 (4*28^2-21^2)h = 28490 cm^3
h = 10.095 cm
H = 40.380 cm (height of 28-cm cone)
H-h = 30.285 (height of 21-cm cone)
the area of the bucket is the area of the 28-cm cone minus the 21-cm cone:
a = pi 28 √(28^2+40.380^2) - pi 21 √(21^2+30.285^2) = 1891 cm^2
subtract the volume of the 21cm cone from a 28-cm cone:
v = 1/3 pi 28^2 H - 1/3 pi 21^2 h
pi/3 (4*28^2-21^2)h = 28490 cm^3
h = 10.095 cm
H = 40.380 cm (height of 28-cm cone)
H-h = 30.285 (height of 21-cm cone)
the area of the bucket is the area of the 28-cm cone minus the 21-cm cone:
a = pi 28 √(28^2+40.380^2) - pi 21 √(21^2+30.285^2) = 1891 cm^2
hmmm. guess I blew it somewhere.
hey I confused
Steve , we both got the same answer of 10.1 for the height of the bucket, so that seems good.
I didn't actually try any calculation for the surface area, simply used the "online calculator", assuming it was correct.
I didn't actually try any calculation for the surface area, simply used the "online calculator", assuming it was correct.
formula for volume frustum of a cone is: 1/3 π h (R² + Rr + r²)
1 liter = 1000 cubic cm
28.49 liters = 28490 cubic cm
1/3 π h (R² + Rr + r²) = 28490
Substitute values to get h and then find l
by s = √((r1 - r2)2 + h2) then substitute l in tsa formula
TSA formula π(R+r)l+πR²+πr²
1 liter = 1000 cubic cm
28.49 liters = 28490 cubic cm
1/3 π h (R² + Rr + r²) = 28490
Substitute values to get h and then find l
by s = √((r1 - r2)2 + h2) then substitute l in tsa formula
TSA formula π(R+r)l+πR²+πr²
h = 15 cm