The ratio of the total surface areas of two cubes is 49 : 81. What is the ratio of their volumes?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 343 : 729
The ratio of the total surface area of the two cubes is 49:81.
the total surface area of the first cube / total surface area of the second cube = 6 × (side of the first cube)2 / 6 × (side of the second cube)2
49/81 = 6 × (side of the first cube)2 6 × (side of the second cube)2
49/81 = (side of the first cube)2 /(side of the second cube)2
7/9 = (side of the first cube)/(side of the second cube) .....Eq.(i)
The ratio of their volumes = (side of first cube)³ / (side of second cube)³
Put Eq.(i) in the above formula.
= (7)3/(9)3
= 343 / 729
= 343 : 729