Question

draw a chart related to "mensuration" of cuboid​

Answer 1

Consider a Cuboid of length, breadth and height to be l, b and h respectively.

Lateral surface area of the cuboid= Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH

=2(b × h) + 2(l × h)

=2h(l + b)

LSA of Cuboid = 2h(l +b)

Volume of the Cuboid

The volume of the cuboid is equal to the product of the area of one surface and height.

Volume of the cuboid = (length × breadth × height) cubic units

Volume of the cuboid = ( l × b × h) cubic units

Surface Area of a Cube

For cube, length = breadth = height

Suppose length of an edge =l

Hence, surface area of the cube = 2(l × l +l × l + l × l) = 2 x 3l2 = 6l2

Total Surface Area of Cube= 6l2

Lateral surface area of a Cube

Formula to find Lateral surface area of the cube is:

2(l × l + l × l) = 4l2

LSA of Cube = 4l2

Volume of the Cube

The volume of the cube is equal to the product of the area of the cube and height. As we know already, all the edges of the cube are of same length. Hence,

Volume of the cube = l2 × h

Since, l = h

Therefore,

Volume of the cube = l2 × l

Volume of the cube = l3

Some More Formulas

Diagonal of the cuboid =√( l2 + b2 +h2)

Perimeter of a cuboid = 4 (l + b + h)

Diagonal of a cube = √3l

Perimeter of a cube = 12l

Example Problems

Example 1: Find the total surface area of cuboid with dimensions 2 inches by 3 inches by 7 inches.

Solution: Total Surface Area(TSA) = 2 (lb + bh + hl )

TSA = 2 ( 2*3 + 3*7 + 7*2)

TSA = 2 ( 6 + 21 + 14 )

TSA = 82

So, the total surface area of this cuboid is 82 inches2

Example 2: The length, width and height of a cuboid are 12 cm, 13 cm and 15 cm respectively. Find the lateral surface area of a cuboid.

Solution: Lateral surface area of a cuboid is given by:

LSA = 2h ( l + w )

LSA = 2*15 ( 12 + 13 )

LSA = 750 cm2

Example 3: Find the surface area of a cube having its sides equal to 8 cm in length.

Solution: Given length, ‘a’= 8 cm

Surface area = 6a2

= 6× 82 = 6 ×64

= 438 cm2

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Frequently Asked Questions

What the difference between cuboid and cube?

A cube is a three-dimensional figure whose all sides are equal i.e. all of its 6 faces are square. On the contrary, a cuboid is a three-dimensional figure whose all sides are not equal and all of its 6 faces are rectangles.

What are the formulas of cube and cuboid?

Total surface area:

Cube= 6× (side)2

Cuboid= 2(lb + bh +lh)

Lateral surface area:

Cube= 4× (side)2

Cuboid= 2h(l +b)

Volume:

Cube= (side)3

Cuboid= (length × breadth × height)

Is a cube a special kind of cuboid?

Yes, a cube is a special kind of cuboid where all the faces of the cuboid are of equal length. In a cuboid, there are 6 faces which are rectangles. If the rectangles have equal sides, they become squares and eventually, the cuboid becomes a cube.

Answer 2

Answer: A cuboid is a 3-D figure formed by six rectangular surfaces and each solid line segment is edge and it edge meets at vertex . Opposite sides and faces are parallel same as rectangle.

Step-by-step explanation:  Mensuration of Cuboid are as follows:

Here, l = length, b =  breadth and h = height

1. Volume of cuboid = l x b x h

2. Surface area of cuboid = 2(lb + bh + hl)

3. Surface area of 4 walls = 2l (b + h )

4. Surface area of cuboid = 2( bh + hl)

5. Diagonal faces of cuboid = 2$\sqrt{l^{2}+b^{2} }$.$\sqrt{b^{2}+h^{2} }$.$\sqrt{h^{2}+l^{2} }$

6. Diagonals of cuboid = $\sqrt{l^{2}+b^{2}+h^{2} }$

7. Height of cuboid = $\frac{volume}{base area}$

8. Area of base  = $\frac{volume}{height}$