Question

A frustum is a cone with the end chop off a bucket in the shape of a frustum has diameters of 10cm and 4cm at its ends and a depth of 3cm calculate the volume of this bucket

Answer 1

The volume of the frustum-shaped bucket with base diameters of 10cm and 4cm and a depth of 3cm is approximately 122.538 cm³.

Step-by-step explanation:

The volume of a frustum of a cone can be calculated by first finding the volume of the larger cone and then subtracting the volume of the smaller cone that was removed. The frustum has circular bases, so we use the formula V = πr²h to compute the volume of each cone. In this case, the diameters of the frustum are 10cm and 4cm, which means the radii are 5cm and 2cm, respectively. The depth (height) of the frustum is 3cm.

To calculate the volume of the full cone before the end was chopped off, we would need the height of that cone, which involves solving for the height using similar triangles. However, since we're not provided that information, we cannot calculate the volume this way. Instead, let's use the formula for the volume of a frustum:

V = ⅓πh(r&sub1;² + r&sub2;² + r&sub1;r&sub2;)

Plugging in the values, we get:

V = ⅓π(3)(5² + 2² + 5×2)

V = ⅓π(3)(25 + 4 + 10)

V = ⅓π(3)(39)

V = π(39)

The value of π is approximately 3.142, so the volume is:

V = 3.142 × 39 cm³

V = 122.538 cm³

Therefore, the volume of the bucket in the shape of a frustum is approximately 122.538 cm³.

Answer 2

The volume of the bucket is 122.52 cm³.

Step-by-step explanation:

Given : A frustum is a cone with the end chop off a bucket in the shape of a frustum has diameters of 10 cm and 4 cm at its ends and a depth of 3 cm.

To find : Calculate the volume of this bucket ?

Solution :

The diameters of frustum is

D=10 cm ⇒ R= 5 cm

d=4 cm ⇒ r= 2 cm

The height is h=3 cm

The volume of the frustum is given by,

`V=(1)/(3)\pi[R^(2) +r^(2) +Rr]h`

Substitute the value in the formula,

`V=(1)/(3)\pi[5^(2) +2^(2) +(5)(2)]3`

`V=(1)/(3)\pi[25+4+10]3`

`V=(1)/(3)\pi[39]3`

`V=39\pi`

`V=122.52`

Therefore, the volume of the bucket is 122.52 cm³.