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

Answer:

The specific weight is $1.5\frac{g}{cm^{3}}$

Step-by-step 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

$V=\frac{1}{3}\pi r^{2}h$

substitute the values

$V=\frac{1}{3}\pi (15)^{2}(8)$

$V=600\pi\ cm^{3}$

step 4

Find the specific weight

Divide the mass by the volume

$\frac{900\pi }{600\pi}=1.5\frac{g}{cm^{3}}$