Question

Find the volume, the total surface area and the lateral surface area of a rectangular solid having :
length = 8.5 m, breadth = 6.4 m and height = 50 cm.​

Answer 1

Before, finding the answer. Let's find out on how we can find the answer.

• As they have mentioned cm in the question, we have to change it to m.
• Now, to find the Volume of Rectangular Solid, we must use the formula of :

$\boxed{ \sf Volume \: of \: Rectangular \: solid = l \times b \times h }$

• To find the Total Surface Area of Rectangular Solid, we must use the formula of :

$\boxed{\sf Rectangular \: Solid \: of \: Total \: Surface \: Area = 2(lb + bh + hl ) }$

• To find the Lateral Surface Area of Rectangular Solid, we must use the formula of :

$\boxed{\sf Lateral \: surface \: area \: of \: Rectangular \: solid = 2h(l+b)}$

___________________

Given :

• Length = 8.5 m
• Breadth = 6.4 m
• Height = 50 cm.​

To find :

• Volume
• Total surface Area
• Lateral surface Area

Solution :

→ Converting from cm to m.

$\sf = 50 \times \dfrac{1}{100}$

= 0.5 m

→ Volume :

Volume of Rectangular solid = l × b × h

                                               = 8.5 × 6.4 × 0.5          

                                               = 27.2 cm³

∴ The Volume of Rectangular Solid is 27.2 cm³.

→ Total surface area :

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

                                   =  2 (8.5 × 6.4) + (6.4 × 0.5) + (0.5 × 8.5)

                                   = 2 (54.4 + 3.2 + 4.25)

                                   = 2 × 61.85

                                   = 123.7 cm²

∴ Total Surface Area of Rectangular Solid is 123.7 cm².

→ Lateral surface area :

Lateral Surface Area = 2h (l + b)

                                   = 2 × 0.5 (8.5 + 6.4)

                                   = 1 × 14.9

                                   = 14.9 cm²

∴ Lateral Surface Area of Rectangular solid is 14.9 cm².