Question

B) The volume of a cuboid is 1200 cm3, its length is 15 cm and breadth is 10 cm, then show that total surface area of the cuboid is 700cm2 ​

Answer 1

Given :

• Volume of Cuboid = 1200 cm³
• Length of Cuboid = 15 cm
• Breadth of Cuboid = 10 cm

To Find :

• Total Surface Area = ?

Solution :

~ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume = Length \times Breadth \times Height }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Total \; Surface \; Area = 2(lb + bh + hl) }}}}}$

Where :

• L = Length
• B = Breadth
• H = Height

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Height :

${\longmapsto{\qquad{\sf{ Volume = Length \times Breadth \times Height }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 1200 = 15 \times 10 \times Height }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 1200 = 150 \times Height }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{1200}{150} = Height }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{1200}{150} = Height }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\red{\pmb{\frak{ Height = 8 \; cm }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Total Surface Area :

${\dashrightarrow{\qquad{\sf{ Total \; Surface \; Area = 2(lb + bh + hl) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Total \; Surface \; Area = 2[(15 \times 10) + (10 \times 8) + (8 \times 15)] }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Total \; Surface \; Area = 2(150 + 80 + 120) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Total \; Surface \; Area = 2 \times 350 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\blue{\pmb{\frak{ Total \; Surface \; Area = 700 \; {cm}^{2} }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Total Surface Area of the given Cuboid is 700 cm² . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

☛ Given :-

☯ Volume of a cuboid = 1200 cm³

☯ Length of a cuboid = 15 cm

☯ Breadth of a cuboid = 10 cm

☛ To Find :-

➔Height of a cuboid = ?

➔ Total Surface Area of Cuboid = ?

☛ Formula used here :-

= > Volume of Cuboid = L×B×W

= > T.S.A of Cuboid = 2(lb+bh+hl)

☛ Solution Start :-

Volume of Cuboid = L×B×H

1200 cm³ = 15 cm × 10 cm × H

1200 cm³ = 150cm² × H

$\frac{1200 \: {cm}^{3} }{150 \: {cm}^{2} } = h$

8 cm = Height

_______________________

Total Surface Area of Cuboid = 2(lb+bh+hl)

T.S.A of Cuboid =2(15×10+10×8+8×15)

T.S.A of Cuboid = 2(150 + 80 + 120)

T.S.A of Cuboid = 2(350)

T.S.A of Cuboid = 2 × 350

T.S.A of Cuboid = 700 cm²

_______________________

Formulas of Cuboid :-

☯ Total Surface Area of Cuboid = 2(lb+bh+hl)

☯ Volume of Cuboid = L×B×W

☯ Lateral Surface Area of Cuboid = 2h(l+b)