Question

The total surface area of a cubical wooden block is 864 cm square Find its lateral surface area and volume ​

Answer 1

Given:

• Total Surface area of cube = 864 cm²

To find:

⟶ Lateral Surface area of cube = ?

⟶ Volume of cube = ?

Method:

Formulas used:

1. TSA of cube = 6s²
2. LSA of cube = 4s²
3. Volume of cube = s³

where s is the side of cube

Let's solve it

TSA of cube = 6s²

⇒ 864 = 6s²

⇒ s² = 864 ÷ 6

⇒ s² = 144

⇒ s = √144

⇒ s = ± 12 cm

Side of cube cannot be negative.

∴ Side = 12 cm

LSA of cube = 4s²

→ LSA = 4 × 12 × 12

→ LSA = 576 cm²

∴ LSA of cube = 576 cm²

Volume of cube = s³

→ Volume = 12 × 12 × 12

→ Volume = 1728 cm²

∴ Volume of cube = 1728 cm²

Answer 2

Correct Question-:

• The total surface area of a cubical wooden block is 864 cm square . Find its lateral surface area and volume.

AnswEr-:

• The Volume of cube = 1728 cm³
• The Lateral Surface Area of Cube -: 576 cm²

EXPLANATION-:

Given -:

• The Total Surface Area of a cubical wooden block is 864 cm square .

To Find -:

• The Lateral Surface Area of Cubical box .
• The Volume of cubical box .

Solution -:

• $\underline{\boxed{\star{\sf{\blue{ Total\:Surface\:Area\:of\:of\:Cube\:  \: = \: 6× Side² }}}}}$

Here -:

• The Total Surface Area of Cube = 864cm²
• The Side of Cube = ??

Now ,

• $\implies{\sf{\large{864 cm² = 6 × Side ²}}}$
• $\implies{\sf{\large{864 ÷ 6 = Side²}}}$
• $\implies{\sf{\large{144 = Side ²}}}$
• $\implies{\sf{\large{\sqrt{144} = Side }}}$
• $\implies{\sf{\large{12 cm = Side }}}$

Therefore,

• The side of a cube = 12 cm

Now -:

☆ The Lateral Surface Area of Cube -:

• $\underline{\boxed{\star{\sf{\blue{ Lateral\:Surface\:Area\:of\:of\:Cube\:  \: = \: 4× Side² }}}}}$

Here,

• The Side of Cube = 12 cm

Now ,

• $\implies{\sf{\large{ 4 × 12 ²}}}$
• $\implies{\sf{\large{ 4 × 144}}}$
• $\implies{\sf{\large{ 576cm²}}}$

Therefore,

• The Lateral Surface Area of Cube -: 576 cm²

☆ The Volume of Cube -:

• $\underline{\boxed{\star{\sf{\blue{ Volume \:of\:of\:Cube\:  \: = \: Side³ }}}}}$

Here,

• The Side of Cube = 12 cm

Now ,

• $\implies{\sf{\large{ 12 ³}}}$
• $\implies{\sf{\large{ 12 × 12 × 12}}}$
• $\implies{\sf{\large{ 1728cm³}}}$

Therefore,

• The Volume of cube = 1728 cm³

• ☆ Figure Related to the question-:
• $\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 12\:cm}\put(13.5,3){\bf\large 12\: cm}\put(-4,5.8){\bf\large 12\:cm}\end{picture}$

_______^_^______________

Hence ,

• The Volume of cube = 1728 cm³
• The Lateral Surface Area of Cube -: 576 cm²

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