10th Class
Mathematics
Surface Areas and Volumes
Question Bank
Surface Area and Volume (Mensuration)
question_answer
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid (formed by adjacent placing of cubes) to that of the sum of the surface areas of the three cubes.
A) \[7:9\]
B) \[49:81\]
C) \[9:7\]
D) \[27:23\]
Correct Answer:
A
Solution :
(a): Let the side of the cube be = a units Total surface area of 3 cubes \[=3\times 6{{a}^{2}}\] \[=18\,\,{{a}^{2}}\] Total surface area of cuboid \[=18\,\,{{a}^{2}}-4{{a}^{2}}=14{{a}^{2}}\] \[\therefore \] Ratio\[=\frac{14{{a}^{2}}}{18{{a}^{2}}}=7:9\]