Question

a manufactuer makes trash cans in the form of a cylinder with a hemphirsical top.The trash can has a height of 70cm. The base radius of both the cylinder and the hemphirscal top is 20cm.

Answer 1

a.) 50cm

b.)
`79588cm^2`

Explanation:

a.) 70-50=20

Answer 2

(a) Total height of cylinder is
`50\ cm`

(b) Total volume of trash can is
`79587.05\ cm^3`

Explanation:

Given

Total height of can is
`70\ cm`

And the base radius of both the cylinder and the hemispherical top is
`20\ cm`.

Let us say,
`r` is the radius of both the cylinder and the hemispherical top

And
`h` is the height of the cylinder.

Part (a)

We need to find total height of cylinder (h), that can be found by subtracting radius of hemispherical top from the total height of can.

So, height of cylinder
`=70-20=50\ cm`

`h=50\ cm`

Part (b)

Now, we will find the total volume of trash can.

The total volume would be sum of volumes of cylinder and hemispherical top.

`=\pi r^2h\ +\ (2)/(3)\pi r^3\\\\=\pi(20)^2* 50\ +\ (2)/(3)\pi(20)^3\\\\=62831.85+16755.2\\\\=79587.05\ cm^3`