The side of a cube is 6 cm. The ratio of its surface area and volume is ___ .

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Solution

$\frac{S u r f a c e A r e a}{V o l u m e} = \frac{6 l^{2}}{l^{3}} = \frac{6 \times 6^{2}}{6^{3}} = 1$

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Q. Question:

Question 8
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Mathematics Surface Areas and Volumes Volume of Solids
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Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

Q. A solid cube of side

12

cm is cut into eight cubes of equal volume. The side of the new cube and the ratio between the surface areas of the two cubes respectively are:

Q. What's the lateral surface area of the cube if the length of its side is 6 cm?

Q. (i) If the Lateral Surface Area of a cube is

900 c m^{2}

, find the length of its side.
(ii) If the Total Surface Area of a cube is

1014 c m^{2}

, find the length of its side.
(iii) The volume of the cube is

125 d m^{3}

. Find its side

A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

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The side of a cube is 6 cm. The ratio of its surface area and volume is ___ .

Surface AreaVolume=6l2l3=6×6263=1

$\frac{S u r f a c e A r e a}{V o l u m e} = \frac{6 l^{2}}{l^{3}} = \frac{6 \times 6^{2}}{6^{3}} = 1$