if the radii of the circular ends of a conical bucket in the shape of frustum of a cone which is 45cm high are 28cm and 7cm.find the capacity of the bucket in litres

v = pi/3 (r^2+R^2+rR)h

= pi/3 (28^2+7^2+28*7)*45
= 15435 pi

15435

To find the capacity of the bucket in liters, we need to find the volume of the frustum of the cone.

The formula to calculate the volume of a frustum of a cone is given by:

V = (1/3) * π * h * (r₁² + r₂² + (r₁ * r₂))

Where:
V is the volume
h is the height of the frustum
r₁ is the radius of the larger circular end
r₂ is the radius of the smaller circular end
π is the mathematical constant pi (approximately 3.14159)

In this case, the height (h) of the frustum is given as 45 cm, the radius of the larger circular end (r₁) is 28 cm, and the radius of the smaller circular end (r₂) is 7 cm.

Now we can calculate the capacity of the bucket:

V = (1/3) * 3.14159 * 45 * (28² + 7² + (28 * 7))

V = (1/3) * 3.14159 * 45 * (784 + 49 + 196)

V = (1/3) * 3.14159 * 45 * 1029

V ≈ 3.14159 * 45 * 343

V ≈ 48242.17155 cubic cm

To convert this volume to liters, we need to divide it by 1000 since there are 1000 cubic centimeters in a liter.

Capacity = 48242.17155 / 1000

Capacity ≈ 48.24217155 liters

Therefore, the capacity of the bucket is approximately 48.242 liters.