If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes will be ?
A. 1 : 3
B. 2 : 3
C. 5 : 9
D. 7 : 9
Answer: Option D
Solution(By Examveda Team)
Let the length of each edge of each cube be aThen, the cuboid formed by placing 3 cubes adjacently has the dimensions 3a , a and a
Surface area of the cuboid :
$$\eqalign{ & = 2\left[ {3a \times a + a \times a + 3a \times a} \right] \cr & = 2\left[ {3{a^2} + {a^2} + 3{a^2}} \right] \cr & = 14{a^2} \cr} $$
Sum of surface area of 3 cubes :
$$\eqalign{ & = \left( {3 \times 6{a^2}} \right) \cr & = 18{a^2} \cr} $$
∴ Required ratio :
$$\eqalign{ & = 14{a^2}:18{a^2} \cr & = 7:9 \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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