Question

Base areas of two prisms are in the. ratio 2:3 and their heights are in the ratio 3:4  a)Find the ratio between their volumes  b) The volume of the first prism is 100 find the volume of the second​

Answer 1

(a) 1:2

(b) 200

Step-by-step explanation:

Given,

The ratio of the base area of the two prisms = 2:3

and

The ratio of the height of two prisms = 3:4

let,

1st prism bass area = 2x, height = 3y

2nd prism bass area = 3x, height = 4y

Now,

(a) we know that,

volume of prism = bass area x height

Now,

The ratio of the volumes of the two prisms

= 1st prism volume/2nd prism volume

= (2x×3y)/(3x×4y)

= 6xy/12xy

= 1/2

= 1:2

(b)

given, 1st prism volume = 100

then, 2nd prism volume = 2×100 = 200