Question

!!!!!!!!!!PLEASE HELP ASAP!!!!!!!!!!

!!!!!!!!!!MY GRADE DEPENDS ON THIS QUESTION!!!!!!!!!!
A silo used to hold grain consits of a cylinder with a height of 25 meters capped by a hemisphere with a diameter of 6 meters. What is the approximate volume of the silo to the nearest cubic meter? Show your work.

Answer 1

The volume of the grain silo, which consists of a cylinder and a hemisphere, is approximately 726 cubic meters when rounded to the nearest cubic meter, using the radius of 3 meters and a height of 25 meters for the cylindrical part.

Step-by-step explanation:

To find the volume of the silo, we need to calculate the volume of both the cylindrical part and the hemispherical cap. We'll start with the cylinder, which has a height of 25 meters.

The diameter of the cylinder and the hemisphere is given as 6 meters, thus the radius (r) is half of that, which is 3 meters.

The formula for the volume of a cylinder is V = πr²h. Substituting the known values (r = 3 meters, h = 25 meters), the calculation for the cylinder's volume is:

V_cylinder = π × (3 m) ² × 25 m = π × 9 m² × 25 m = 225π m³.

Next, for the hemisphere's volume, we use the formula for a sphere's volume divided by two since a hemisphere is half a sphere. The formula for a sphere's volume is V = ⅔πr³. Therefore, the volume of the hemisphere is:

V_hemisphere = (⅔π × (3 m)³) / 2 = (4π × 27 m³) / 6 = 36π m³ / 6 = 6π m³.

Adding both volumes gives us the total volume of the silo:

V_total = V_cylinder + V_hemisphere = 225π m³ + 6π m³ = 231π m³.

Using 3.142 as an approximation for π, the volume to the nearest cubic meter is approximately:

V_total ≈ 231 × 3.142 m³ = 725.922 m³, which rounds to 726 m³.

Answer 2

Look at the picture.

The formula of the volume of a cylinder:


`V_C=\pi r^2H`

We have:


`d=6m;\ d=2r\to r=3m\\H=25m`

Substitute:


`V_C=\pi\cdot3^2\cdot25=225\pi\ m^3`

The formula of the volume of a sphere:


`V_S=(4)/(3)\pi r^3`

We have a hemisphere, therefore the formula of the volume is:


`V_H=(1)/(2)V_S=(1)/(2)\cdot(4)/(3)\pi r^3=(2)/(3)\pi r^3`

We have:


`r=3m`

Substitute:


`V_H=(2)/(3)\pi\cdot3^3=(2)/(3)\pi\cdot27=2\pi\cdot9=18\pi\ m^3`

The volume of a silo:


`V=V_C+V_H\to V=225\pi+18\pi=243\pi\ m^3\approx243\cdot3.14\approx763\ m^3`

Answer: 763 m³.