If the volume of a cube is $216 c m^{3}$ , then the surface area of the cube will be

214 c m^{2}

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216 c m^{2}

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218 c m^{2}

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220 c m^{2}

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Solution

The correct option is C $216 c m^{2}$
Volume $= 216 c m^{3} \Rightarrow (E d g e)^{3} = 216$
$\Rightarrow E d g e = \sqrt[3]{216} = 6 c m$
$∴$ Surface area $= 6 \times (e d g e)^{2} = 6 \times (6)^{2} c m^{2}$
$= 216 c m^{2}$ .

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Similar questions

Q. The total surface area of a cube is

216 c m^{2}

216cm2. Find its volume in cm

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Q. If the volume of a cube is

3 \sqrt{3} a^{3}

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Q. The volume of a cube whose surface area is 96 cm², is

(a)

16 \sqrt{2} c m^{3}

(b) 32 cm³

(c) 64 cm³

(d) 216 cm³

Find the surface area of a cube whose volume is $216 c m^{3}$ .

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

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If the volume of a cube is 216cm3, then the surface area of the cube will be

The correct option is C 216cm2Volume =216cm3⇒(Edge)3=216⇒Edge=3√216=6cm ∴ Surface area =6×(edge)2=6×(6)2cm2=216cm2.

If the volume of a cube is $216 c m^{3}$ , then the surface area of the cube will be

The correct option is C $216 c m^{2}$
Volume $= 216 c m^{3} \Rightarrow (E d g e)^{3} = 216$
$\Rightarrow E d g e = \sqrt[3]{216} = 6 c m$
$∴$ Surface area $= 6 \times (e d g e)^{2} = 6 \times (6)^{2} c m^{2}$
$= 216 c m^{2}$ .