Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid os $648 {c m}^{2}$ ; find the length of edge of each cube.
Also find the ratio between the surface area of the resulting cuboid and the surface area of a cube.

Open in App

Solution

Let the length of the edge of each cube $= l$
The length of the resulting cuboid $= 4 \times l = 4 l c m$
Let width $(b) = l c m$
Lte height $(h) = l c m$
The total surface area of the resulting cuboid $= 2 (l \times b + b \times h + h \times l)$
$648 = 2 (4 l \times l + l \times l + l \times 4 l)$
$4 l^{2} + l^{2} + 4 l^{2} = 324$
$9 l^{2} = 324$
$l^{2} = 36$
$l = 6 c m$
Therefore, the length of each cube is $6 c m$ .
$\frac{S u r f a c e a r e a o f t h e r e s u l t i n g c u b o i d}{S u r f a c e a r e a o f t h e c u b e} = \frac{648}{6 l^{2}}$
$\frac{S u r f a c e a r e a o f t h e r e s u l t i n g c u b o i d}{S u r f a c e a r e a o f t h e c u b e} = \frac{648}{6 (6)^{2}}$
$\frac{S u r f a c e a r e a o f t h e r e s u l t i n g c u b o i d}{S u r f a c e a r e a o f t h e c u b e} = \frac{648}{216} = \frac{3}{1} = 3 : 1$

Suggest Corrections

Similar questions

648

c m^{2};

648

c m^{2}

Two cubes, each of edge length 12 cm are joined end to end. Find the surface area of the resulting cuboid.

Join BYJU'S Learning Program