A bucket is 12cm in diameter at the top,8cm in diameter at the bottom and 4cm deep.calculate the volume.
You can consider the volume of the whole cone, minus the part that has been chopped off to leave the bucket.
Or, you can use the handy formula V = πh/3 (R^2+rR+r^2)
v = 1/3 π*4(12^2 + 12*8 + 8^2)
the bucket is a partial cone
if the sides were extended downward
... the entire cone would be 12 cm deep ... 4 cm / [1 - (8 cm / 12 cm)]
the volume of the entire cone would be ... 1/3 * π * (6 cm)^2 * 12
the volume of the extension would be ... 1/3 * π * (4 cm)^2 * 8
the volume of the bucket is the difference ... entire minus extension
To calculate the volume of a bucket, you can use the formula for the volume of a frustum of a cone:
V = (π * h/3) * (R^2 + r^2 + R*r)
where:
V = Volume
π = Pi (approximately 3.14159)
h = Height of the frustum
r = Radius of the smaller circular base
R = Radius of the larger circular base
In this case, the height of the frustum (bucket depth) is given as 4 cm, the radius of the smaller circular base (bottom diameter/2) is 8/2 = 4 cm, and the radius of the larger circular base (top diameter/2) is 12/2 = 6 cm.
Substituting these values into the formula:
V = (π * 4/3) * (6^2 + 4^2 + 6*4)
Simplifying:
V = (π * 4/3) * (36 + 16 + 24)
V = (π * 4/3) * 76
V ≈ 3.14159 * 4/3 *76
V ≈ 4.188 * 76
V ≈ 322.048 cubic centimeters
Therefore, the volume of the bucket is approximately 322.048 cubic centimeters.
To calculate the volume of the bucket, you need to calculate the volume of a frustum.
To get the volume of a frustum, you can use the following formula:
Volume = (1/3) * π * h * (r₁² + r₂² + r₁*r₂)
Here,
- h is the height of the frustum (depth of the bucket)
- r₁ is the radius of the top of the frustum (diameter at the top divided by 2)
- r₂ is the radius of the bottom of the frustum (diameter at the bottom divided by 2)
- π is a mathematical constant approximately equal to 3.14159
In this case,
- h = 4cm
- r₁ = (12cm / 2) = 6cm
- r₂ = (8cm / 2) = 4cm
Now, using the formula, we can calculate the volume of the bucket:
Volume = (1/3) * π * 4cm * (6² + 4² + 6cm * 4cm)
= (1/3) * π * 4cm * (36cm² + 16cm² + 24cm²)
= (1/3) * π * 4cm * 76cm²
= (4/3) * π * 4cm * 76cm²
= (16/3) * 76π cm³
≈ 804 cm³ (approximately)
Therefore, the volume of the bucket is approximately 804 cm³.