# CLASS-8CUBE & CUBOID - PROBLEM & SOLUTION

Example.1) The dimension of a cuboid are 15 cm, 12 cm, and 18 cm. Find the diagonal of the said cuboid.

Ans.)  Here, l = 15 cm, b = 12 cm, h = 18 cm

As we all know the length of a diagonal of a cuboid = √(l² + b² + h²)                                                                                                    =  √(15² + 12² + 18²)

=  √(225 + 144 + 324)

=  √693 =  26.32 cm (approximately)     (Ans.)

Example.2) The dimension of a cuboid are in the ratio 3 : 5 : 7 and its surface area is 9088 m². Find its (a) length, breadth, & height, (b) its volume.

Ans.) as per the given condition length : breadth : height =  3 : 5 : 7

l                b              h

Let,   --------- =  ---------- = --------- =  y cm

3                5              7

So, l = 3y, b = 5y, and h = 7y

As we all know the formula for  the surface area of the cuboid

= 2 (lb + bh + hl)

= 2{(3y X 5y) + (5y X 7y) + (7y X 3y)}                                                                                                                           =  2 (15y² + 35y² + 21y²) = 2 X 71y²                                                                                                                         =  142 y²

Given,  142 y² =  9088

Or,      y² =  64

Or,      y  =  √64 =  √8²

Or,      y = 8

So, Length = 3y = 3 X 8 = 24 cm

Breadth = 5y = 5 X 8 = 40 cm

Height = 7y = 7 X 8 = 56 cm ………………………………..(a)     (Ans.)

The volume of the cuboid = l X b X h

= 24 cm X 40 cm X 56 cm

= 53760 cmᶟ ……………………..(b)     (Ans.)

Example.3) The length of a diagonal of a cube is 11√3 cm. If length = 8 cm and breadth = 10 cm then find the height.

Ans.) as per the given condition, length = 8 cm and breadth = 10 cm.

let, height = H

so, as per the formula or rules we have = √ (l² + b² + h²)

so,   √ (l² + b² + h²) =  11√3

so,  {√ (l² + b² + h²)}² = (11√3)²     [put square on both side]

so,    l² + b² + h² =  363

so,    8² + 10² + H² = 363

so,    H² = 363 – (64 + 100) = 363 – 164 = 199

so,    H = √ 199 =  14.10  (approximately)

so the required height of the said cuboid is 14.10 cm   (Ans.)

Example.4) If a side of a cuboid is 8 cm. find (a) its volume, (b) its surface area, (c) its lateral surface area, and (d) the length of its diagonal.

Ans.)  the volume of the cube = (length of a side)ᶟ

= (8 cm)ᶟ = 512 cmᶟ ……………….(a)

Its surface area = 6 X (length of a side)²

= 6 X (8 cm)² = 6 X 64 cm² = 384 cm²…………….(b)

The lateral surface area of a cube = 4 X (length of a side)²

= 4 X (8 cm)² =  256 cm²………………..(c)

The length of its diagonal = √3 X length of a side

= √3 X 8 cm = 8√3 cm……………….(d)   (Ans.)