Question

e) If the total surface area of a cuboid is 432 ma and the ratio of length, breadth and
height is 6:4:3, then height of the cuboid is
() 24 m
(ii) 16 m
(iii) 6 m
(iv) 4 m​

Answer 1

Answer:

(iii) 6 m ✔

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• TSA of cuboid = 432 m²
• Ratio of l, b and h = 6:4:3

$\underline{\bigstar\:\textsf{To\:find:}}$

• Height = ?

$\underline{\bigstar\:\textsf{Solution:}}$

Let the length be 6x, breadth be 4x and height be 3x.

We are given with the TSA of cuboid. We know that $\pink{\sf{TSA\:of\:cuboid\:=\:2(lb\:+\:bh\:+\:hl).}}$

(Putting value for x)

$\longrightarrow$ 432 = 2(6x × 4x + 4x × 3x + 3x × 6x)

$\longrightarrow$ 216 = 24x² + 12x² + 18x²

$\longrightarrow$ 216 = 54x²

$\longrightarrow\:\sf{\cancel\dfrac{216}{54}\:=\:x^2}$

$\longrightarrow$ 4 = x²

$\longrightarrow\:\sf{\sqrt{4}\:=\:x}$

$\longrightarrow$ 2 = x

We have found the value of x i.e, 2.

So, the length = 6x = 6 × 2 = 12 m

breadth = 4x = 4 × 2 = 8 m

height = 3x = 3 × 2 = 6 m

${\large{\boxed{\sf{\therefore \:Height\:is\:6\:m}}}}$