If the radii of the circular ends of a conical bucket,which is 45cm high,are 28cm and 7cm.Find the capacity of the bucket?
Can u plz answer this question fast!!!!
consider the top of a large cone which has been cut off to leave the frustrum. Draw a side view. Using similar triangles, we know that the top of the bucket is 3/4 as high as the uncut cone. So, the piece that was cut off has an altitude of 15 cm.
Subtract the small top of the cone from the whole cone to get the volume of the bucket:
π/3 * 28^2 * 60 - π/3 * 7^2 * 15 = 15435π cm^3
To find the capacity of the bucket, we need to determine the volume of the conical shape. The formula for the volume of a cone is given by:
Volume = (1/3) * π * r^2 * h
Where:
- π is the mathematical constant, approximately equal to 3.14159
- r is the radius of the circular base
- h is the height of the cone
In this case, we are given two radii: 28cm and 7cm. However, since the shape of the bucket is conical, we need to use the radius of the larger circular end (28cm) as the base of the cone.
Substituting the values into the formula, we have:
Volume = (1/3) * π * (28cm)^2 * 45cm
Now, let's calculate the volume:
Volume = (1/3) * 3.14159 * (28cm)^2 * 45cm
Volume = 3.14159 * 784cm^2 * 45cm / 3
Volume = 3.14159 * 28,056cm^3
Volume = 88,184.64cm^3
Therefore, the capacity of the bucket is approximately 88,184.64 cubic centimeters (or cm^3).