Question

*If a cuboidal room is 10 meters long, 8.5 meters wide and 12 meters high, what is its volume?*

1️⃣ 10.20 m
2️⃣ 1020 cucm
3️⃣ 1020 cu.m
4️⃣ 120 cucm

Answer 1

Given :-

Measurements of the cuboidal room :-

• Length = 10m
• Breadth = 8.5m
• Height = 12m

To find :-

Volume of the cuboid

Volume of cuboid :-

Length × Breadth × Height

By substituting the values,

Volume = 10m × 8.5m × 12m

VOLUME = 1,020m³

Hence option (3) 1020m³ is correct

HOW TO FIND TOTAL SURFACE AREA and LATERAL SURFACE AREA :-

Total surface area :-

• The total surface area of a shape is it's entire outer surface area.

2[(length×breadth)+(Breadth×height)+(height×length)]

Substituting the values,

T.S.A = 2[(10×8.5)+(8.5×12)+(10×12)]

T.S.A = 2(85+102+120)

T.S.A = 2(307)

Total surface area of the cuboid = 614m²

Lateral surface area :-

• The area of the shape excluding it's top and bottom is called the shape's lateral surface area

(2×height×length) + (2×height×breadth)

=≥ 2 × height (length + breadth) or Perimeter of base × height

Substituting the values,

L.S.A = 2×12(10+8.5)

L.S.A = 24(18.5)

Lateral surface area of the cuboid = 444m²

The longest pole :-

In a cuboidal room the longest pole or rod that can be placed is the diagonal of the room.

To calculate the length of the diagonal, we have to use the formula :-

$\sqrt{ {length}^{2} + {breadth}^{2} + {height}^{2} }$

Let us calculate with the measurements given.

$length \: of \: the \: diagonal = \sqrt{ {10}^{2} + {8.5}^{2} + {12}^{2} }$

$= \sqrt{100 +72.25 + 144}$

$= \sqrt{316.25}$

$diagonal = \sqrt{316.25m}$

Some more formulas :-

Total surface area of a cube = 6a²

Lateral surface area of a cube = 4a²

Volume of a cube = a³

Total surface area of a cylinder = 2πrh + 2πr² =≥ 2πr(h+r)

Lateral surface area of a cylinder = 2πrh

Volume of the cylinder = πr²h

Answer 2

Answer:

10.20m is the answer of this question