Question

Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?

Answer 1

Answer:

The ratio of the volumes of two cones is 3 : 1.

Step-by-step explanation:

Let the heights of two cones h1 & h2 and radii be r1 & r2.

Given :

Two cones have their heights in the ratio 1 : 3 & radii 3 : 1.

Let Heights of two cones be h1 = 1a , h2 =  3a &  Radii of two cones be  r1 = 3b ,  r2 = 1b

Volume of first cone (V1) / Volume of second cone(V2) = ⅓ πr1²h1/ ⅓ πr2²h2

V1/V2 = ⅓ πr1²h1/ ⅓ πr2²h2

V1/V2 = r1²h1/r2²h2

V1/V2 = r1²/ r2² × h1/h2

V1/V2 = (3b/1b)² × (1a/3a)

V1/V2 = 9/1 × ⅓

V1/V2 = 3/1  

V1 : V2 = 3 : 1

Hence, the ratio of the volumes of two cones is 3 : 1.

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

HOLA!!!

Let us take height of the first cone as h1 and height of the second cone as h2 .

Also,let's take the radius of the first cone r1 and radius of the second cone as r2 .

Volume of 1st cone :-

$(1 \div 3) {\pi} {(r1)}^{2}( h1)$

Volume of 2nd cone :-

$(1 \div 3)\pi {(r2)}^{2} (h2)$

Ratio =

$((1 \div 3)\pi( {r1)}^{2} (h1)) \div ((1 \div 3)\pi {(r2)}^{2} (h2))$

$= ({(r1)}^{2} (h1)) \div (( {r2)}^{2}(h2) )$

$= ( ({r1)}^{2} \div {(r2)}^{2} ) \times (h1 \div h2)$

$= (3 \div 1) {}^{2} \times (1 \div 3)$

=3:1

HOPE IT HELPS UHH #CHEERS