Question

The radii of the circular ends (bases) of a 45-cm high bucket (which is in the form of an inverted frustum) are 28 cm and 7 cm. What is the capacity of the bucket in cubic centimeters?

Answer 1

The capacity of a bucket in the form of an inverted frustum with radii of 28 cm and 7 cm, and a height of 45 cm, is approximately 48176.335 cm³.

Step-by-step explanation:

The question asks us to find the capacity of the bucket in cubic centimeters, which is in the form of an inverted frustum. The bucket has a height of 45 cm with radii of its circular ends being 28 cm and 7 cm. To find its capacity, we use the formula for the volume of a frustum of a cone:

V = \( \frac{1}{3}\pi h (r1^2 + r2^2 + r1*r2) \)

Here, \(h\) is the height of the frustum, \(r1\) and \(r2\) are the radii of the two circular bases. Substituting the given values:

V = \( \frac{1}{3}\pi (45) (28^2 + 7^2 + 28*7) \)

Calculating further we get:

V = \( \frac{1}{3}\pi (45) (784 + 49 + 196) = \frac{1}{3}\pi (45) (1029) = \pi (45) (343) = 15345\pi \)

Using \(\pi \approx 3.14159\), we get:

V = 15345 * 3.14159 which yields approximately \(48176.335 cm^3\), which is the capacity of the bucket.