Question

5. Find the volume and surface area of the cube having an edge :
(i) 7 cm
(ii) 4 m
(iii) 2.5 cm
(iv) 4.5 cm
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Answer 1

A n s w e r

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G i v e n

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Edges of cube -

• (i) 7 cm
• (ii) 4 m
• (iii) 2.5 cm
• (iv) 4.5 cm

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F i n d

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• Volume and surface area of the cube in each case

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S o l u t i o n

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$\underline{ \underline{\bold{\texttt{Volume of cube :}}}}$

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➠ V = e³ ⚊⚊⚊⚊ ⓵

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Where ,

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• V = Volume of cube

• e = Edge of cube

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$\underline{ \underline{\bold{\texttt{Total surface area :}}}}$

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➠ S = 6e² ⚊⚊⚊⚊ ⓶

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Where ,

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• S = Total surface area of cube

• e = Edge of cube

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For (i) 7 cm

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⟮ Putting e = 7 cm in ⓵ ⟯

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: ➜ V = 7³

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: : ➨ V = 343 cu. cm

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• Hence the volume of cube having 7 cm edge is 343 cu. cm

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⟮ Putting e = 7 cm in ⓶ ⟯

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: ➜ S = 6e²

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: ➜ S = 6(7)²

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: ➜ S = 6(49)

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: : ➨ S = 294 sq. cm

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• Hence the total surface area of cube having 7 cm edge is 294 sq. cm

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For (ii) 4 m

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⟮ Putting e = 4 m in ⓵ ⟯

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: ➜ V = 4³

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: : ➨ V = 64 cu. m

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• Hence the volume of cube having 4 m edge is 64 cu. m

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⟮ Putting e = 4 m in ⓶ ⟯

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: ➜ S = 6e²

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: ➜ S = 6(4)²

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: ➜ S = 6(16)

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: : ➨ S = 96 sq. m

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• Hence the total surface area of cube having 4 m edge is 96 sq. m

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For (iii) 2.5 cm

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⟮ Putting e = 2.5 cm in ⓵ ⟯

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: ➜ V = (2.5)³

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: : ➨ V = 15.625 cu. cm

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• Hence the volume of cube having 2.5 cm edge is 15.625 cu. cm

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⟮ Putting e = 2.5 cm in ⓶ ⟯

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: ➜ S = 6e²

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: ➜ S = 6(2.5)²

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: ➜ S = 6(6.25)

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: : ➨ S = 37.5 sq. cm

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• Hence the total surface area of cube having 2.5 cm edge is 37.5 sq. cm

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For (iv) 4.5 cm

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⟮ Putting e = 4.5 cm in ⓵ ⟯

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: ➜ V = (4.5)³

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: : ➨ V = 91.125 cu. cm

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• Hence the volume of cube having 4.5 cm edge is 91.125 cu. cm

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⟮ Putting e = 4.5 cm in ⓶ ⟯

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: ➜ S = 6e²

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: ➜ S = 6(4.5)²

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: ➜ S = 6(20.25)

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: : ➨ S = 121.5 sq. cm

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• Hence the total surface area of cube having 4.5 cm edge is 121.5 sq. cm

Answer 2

G i v e n

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• Edges of cube -

• (i) 7 cm
• (ii) 4 m
• (iii) 2.5 cm
• (iv) 4.5 cm

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F i n d

$\:\:$

• Volume and surface area of the cube in each case

$\:\:$

S o l u t i o n

$\:\:$

$\underline{ \underline{\bold{\texttt{Volume of cube :}}}}$

$\:\:$

➠ V = e³ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

V = Volume of cube

e = Edge of cube

$\:\:$

$\underline{ \underline{\bold{\texttt{Total surface area :}}}}$

$\:\:$

➠ S = 6e² ⚊⚊⚊⚊ ⓶

$\:\:$

Where ,

$\:\:$

S = Total surface area of cube

e = Edge of cube

$\:\:$

For (i) 7 cm

$\:\:$

⟮ Putting e = 7 cm in ⓵ ⟯

$\:\:$

: ➜ V = 7³

$\:\:$

: : ➨ V = 343 cu. cm

$\:\:$

Hence the volume of cube having 7 cm edge is 343 cu. cm

$\:\:$

⟮ Putting e = 7 cm in ⓶ ⟯

$\:\:$

: ➜ S = 6e²

$\:\:$

: ➜ S = 6(7)²

$\:\:$

: ➜ S = 6(49)

$\:\:$

: : ➨ S = 294 sq. cm

$\:\:$

Hence the total surface area of cube having 7 cm edge is 294 sq. cm

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For (ii) 4 m

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⟮ Putting e = 4 m in ⓵ ⟯

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: ➜ V = 4³

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: : ➨ V = 64 cu. m

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Hence the volume of cube having 4 m edge is 64 cu. m

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⟮ Putting e = 4 m in ⓶ ⟯

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: ➜ S = 6e²

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: ➜ S = 6(4)²

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: ➜ S = 6(16)

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: : ➨ S = 96 sq. m

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Hence the total surface area of cube having 4 m edge is 96 sq. m

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For (iii) 2.5 cm

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⟮ Putting e = 2.5 cm in ⓵ ⟯

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: ➜ V = (2.5)³

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: : ➨ V = 15.625 cu. cm

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Hence the volume of cube having 2.5 cm edge is 15.625 cu. cm

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⟮ Putting e = 2.5 cm in ⓶ ⟯

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: ➜ S = 6e²

$\:\:$

: ➜ S = 6(2.5)²

$\:\:$

: ➜ S = 6(6.25)

$\:\:$

: : ➨ S = 37.5 sq. cm

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Hence the total surface area of cube having 2.5 cm edge is 37.5 sq. cm

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For (iv) 4.5 cm

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⟮ Putting e = 4.5 cm in ⓵ ⟯

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: ➜ V = (4.5)³

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: : ➨ V = 91.125 cu. cm

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Hence the volume of cube having 4.5 cm edge is 91.125 cu. cm

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⟮ Putting e = 4.5 cm in ⓶ ⟯

$\:\:$

: ➜ S = 6e²

$\:\:$

: ➜ S = 6(4.5)²

$\:\:$

: ➜ S = 6(20.25)

$\:\:$

: : ➨ S = 121.5 sq. cm

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Hence the total surface area of cube having 4.5 cm edge is 121.5 sq. cm