Answer:
A) 480cm^3
B) 35 cm^2
Step-by-step explanation:
Given two similar solids
Volume of A = 60cm^3
Surface area of B = 140cm^2
Side A = 3
Side B = 6
NB: if two solids are similar, the ratio of their volume equals the cube of the corresponding proportion of their linear measure.
That is :
Volume A / volume B = (side A / side B)^3
(60 / volume B) = (3 / 6)^3
(60 / volume B) = (1/2)^3
(60 / volume B) = (1/8)
Volume B = 480cm^3
B) the surface area:
NB: if two solids are similar, the ratio of their surface areas equals the square of the corresponding proportion of their linear measure.
Surface area A / surface area B = (side A / side B)^3
(surface area A / 140) = (3 / 6)^2
(surface area A / 140) = (1/2)^2
(surface area A / 140) = 1/4
4 × surface area A = 140
Surface area A = 140/4
Surface area of A = 35cm^2
