Question

9. The surface area of a cuboid is 468 cm². Its length and breadth are 12 cm and 9 cm respectively
Find its height.​

Answer 1

Given :–

• Surface area of a cuboid = 468cm²
• Length of a cuboid (l) = 12cm
• Breadth of a cuboid (b) = 9cm

To Find :–

• Height of a cuboid.

Solution :–

Let, the height of a cuboid be x.

We know that,

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

• l = 12cm
• b = 9cm

Now, put the given values in the formula of surface area of a cuboid.

⟹ 468cm² = 2[(12)(9) + (9)(x) + (x)(12)]

Open the small brackets.

⟹ 468cm² = 2[108 + 9x + 12x]

⟹ 468cm² = 2[108 + 21x]

Now, open the large bracket.

⟹ 468cm² = 216 + 42x

⟹ 468 – 216 = 42x

⟹ 252 = 42x

⟹ $\dfrac{\cancel{252}}{\cancel{42}}$ = x

Cut the denominator and the numerator by 2, we obtain

⟹ $\dfrac{\cancel{126}}{\cancel{21}}$ = x

Cut the denominator and the numerator by 3, we obtain

⟹ $\dfrac{\cancel{42}}{\cancel{7}}$ = x

Cut the denominator and the numerator by 7, we obtain

⟹ 6 = x

Hence,

Height of a cuboid is 6cm.

Check :–

Surface area = 2(lb + bh + hl)

• Surface area of a cuboid = 468cm²
• Length of a cuboid = 12cm
• Breadth of a cuboid = 9cm
• Height of a cuboid = 6cm

Now, put all the values in the formula of surface area of a cuboid.

⟹ 2[(12)(9) + (9)(6) + (6)(12)]

Now, solve the small brackets.

⟹ 2[108 + 54 + 72]

⟹ 2[234]

Now, open the large bracket.

⟹ 468cm²

The surface area of a cuboid is equal to the given surface area value. So, the answer is correct.

Answer 2

Answer:

6 cm

Step-by-step explanation:

length = 12cm

breadth =9cm

height = ?

surface area of cuboid = 468cm²

2*( lb+bh+hl) = 468cm²

2*( 12 +9+9+h+h+12) =468cm²

2*( 21+9h+12h)= 468cm²

108+21h = 468/2

21 h = 234 - 108

21h = 126

h = 126/21

h =6cm