Question

Un cono ha l'area laterale di 255 pigreco cm^2, l'apotema di 17 cm e pesa 900 pigreco g. Calcola il peso specifico del materiale di cui è costituito

Answer 1

The specific weight is
`1.5(g)/(cm^(3))`

Explanation:

The question in English

A cone has a lateral area of 255 pi cm^2, an apothem of 17 cm and weighs 900 pi g. It calculates the specific weight of the material of which it is composed

step 1

Find the radius of the cone

we know that

The lateral area of a cone is equal to

`LA=\pi rl`

we have

`LA=255\pi\ cm^(2)`

`l=17\ cm`

substitute the values

`255\pi=\pi r(17)`

Simplify

`255=r(17)`

`r=255/(17)=15\ cm`

step 2

Find the height of the cone

Applying the Pythagoras Theorem

`l^(2) =r^(2) +h^(2)`

substitute the values and solve for h

`17^(2) =15^(2) +h^(2)`

`h^(2)=17^(2)-15^(2)`

`h^(2)=64`

`h=8\ cm`

step 3

Find the volume of the cone

The volume of the cone is equal to

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

substitute the values

`V=(1)/(3)\pi (15)^(2)(8)`

`V=600\pi\ cm^(3)`

step 4

Find the specific weight

Divide the mass by the volume

`(900\pi )/(600\pi)=1.5(g)/(cm^(3))`