Ratio of volume and total surface area of a cube of side length 6 m is .

1 : 1

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2 : 1

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1 : 2

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1 : 3

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Solution

The correct option is A 1 : 1
Volume of a cube = (side $)^{3}$ = $6^{3} = 216 m^{3}$
Total surface area of a cube
$= 6 \times$ Area of the base
Area of the base $= 6^{2} = 36$
Total surface area $= 6 \times 36 = 216 m^{2}$
Ratio = 216 : 216 = 1 : 1

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Q. A solid cube of side 12 cm is cut into eight cubes of equal volume. Find the ratio between their surface areas.

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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

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Ratio of volume and total surface area of a cube of side length 6 m is .

The correct option is A 1 : 1Volume of a cube = (side)3 = 63=216 m3 Total surface area of a cube =6× Area of the base Area of the base =62=36 Total surface area =6×36=216 m2 Ratio = 216 : 216 = 1 : 1

The correct option is A 1 : 1
Volume of a cube = (side $)^{3}$ = $6^{3} = 216 m^{3}$
Total surface area of a cube
$= 6 \times$ Area of the base
Area of the base $= 6^{2} = 36$
Total surface area $= 6 \times 36 = 216 m^{2}$
Ratio = 216 : 216 = 1 : 1