Question

A cone-shaped pile of gravel has a diameter of 30 m and a height of 9.1 m.

Which estimate best approximates the volume of the pile of gravel?

2120 m³

2600 m³

6360 m³

8480 m³

Answer 1

d/2=r
vcone=(1/3)hpir^2
given
d=30
h=9.1
d/2=30/2=15=r

v=(1/3)9.1pi15^2
v=(9.1/3)pi225
v=682.5pi
use 3.141592 to aprox pi
v=2144.13654
the closese is the first one
answer would be 2120 m³

Answer 2

Answer: The correct option is (A) 2120 m³.

Step-by-step explanation: Given that a cone-shaped pile of gravel has a diameter of 30 m and a height of 9.1 m.

We are to select the correct option that estimate best approximates the volume of the pile of gravel.

The VOLUME of a cone with radius 'r' units and height 'h' units is given by the formula:

`V=(1)/(3)\pi r^2h.`

In the given cone-shaped pile, diameter of gravel is 30 m, so its radius will be

`r=(30)/(2)=15~\textup{m},`

and height, h = 9.1 m.

Therefore, the volume of the cone-shaped pile is

`V\\\\\\=(1)/(3)\pi r^2h\\\\\\=(1)/(3)* 3.14 * 15^2* 9.1\\\\\\=3.14* 75* 9.1\\\\=2143.05~\textup{m}^3[approx].`

Out of the given options, only 2120 is the nearest one, so the best approximate will be 2120 m³.

Thus, (A) is the correct option.