Question

The volume of a cuboid is 420 cubic cm. Find the surface area of ​​the cuboid if its breadth and height are 7 cm and 5 cm respectively.​

Answer 1

Answer:

TSA of cuboid = 358 cm²

Step-by-step explanation:

Given:

• Volume of cuboid = 420 cm³
• Breadth = 7 cm
• Height = 5 cm

To find:

Surface area of cuboid = ?

Formulas used:

1. Volume of cuboid = lbh
2. TSA of cuboid = 2 (lb + bh + hl)

Solution:

First, let's find out the length of the cuboid.

Volume of cuboid = lbh

➝ 420 = length × 7 × 5

➝ 420 = length × 35

➝ Length = 420 ÷ 35

➝ Length = 12 cm

Now, for finding the surface area;

TSA of cuboid = 2 (lb + bh + hl)

➝ TSA of cuboid = 2 [(12)(7) + (7)(5) + (5)(12)]

➝ TSA of cuboid = 2 [84 + 35 + 60]

➝ TSA of cuboid = 2 (179)

➝ TSA of cuboid = 358 cm²

∴ TSA of cuboid = 358 cm²

Answer 2

Given :

• Volume of Cuboid = 420 cm³
• Breadth of Cuboid = 7 cm
• Height of Cuboid = 5 cm

$\\ \rule{200pt}{3pt}$

To Find :

• Surface Area of Cuboid = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ Formula Used :

• Volume :

${\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{\frak{ Volume{\small_{(Cuboid)}} = L \times W \times H }}}}}}}}$

• Surface Area :

${\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{\frak{ TSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}}}}$

Where :

• ➻ L = Length
• ➻ B = Breadth or Width
• ➻ H = Height
• ➻ TSA = Total Surface Area

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

~ Calculating the Length of Cuboid :

${\longmapsto{\qquad{\sf{ Volume{\small_{(Cuboid)}} = L \times W \times H }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 420 = L \times 7 \times 5 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 420 = L \times 35 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{420}{35} = L }}}} \\ \\ \ {\qquad{\textsf{ Length of the Cuboid = {\red{\sf{ 12 \: cm }}}}}}$

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

~ Calculating the Surface Area :

${:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2[(12 \times 7) + (7 \times 5) + (5 \times 12)] }}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2(84 + 35 + 60)}}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2 \times 179 }}}} \\ \\ \ {\qquad{\textsf{ Surface Area of the Cuboid = {\green{\sf{ 358 \: cm² }}}}}}$

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

Therefore :

❝ Surface Area of the given Cuboid is 358 cm² . ❞

$\\ {\orange{\underline{\rule{75pt}{9pt}}}}{\gray{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}$