Question

the dimensions of a closed cuboid are in the ratio 5 is to 4 is to 3 if the total surface area is 0.94 metre square find the dimensions of the cuboid​

Answer 1

ok

let

length is 5x

breadth is 4x

height is 3x

total surface area

=2(lb+bh+hl)

=2(20x^2+12x^2+15x^2)

=2(47x^2)

so

0.94=2×47x^2

94/100=2x^2

(94)/200×47=x^2

2/200=x^2

0.01=x^2
x=0.1


dimensions are

length 0.5m

breadth 0.4m

height 0.3m

Answer 2

Given - Dimensions of the closed cuboid are in the ratio 5 : 4 : 3

Let the common ratio be : R

Dimensions of the closed cuboid are :

★  Length = 5R

★  Breadth = 4R

★  Height = 3R

Given : The Total Surface Area is 0.94 m²

We know that - Total Surface Area of a Cuboid is given by :

★  2(Length × Breadth + Breadth × Height + Height × Length)

$\longrightarrow$  2(5R × 4R + 4R × 3R + 3R × 5R) = 0.94

$\longrightarrow$  2(20R² + 12R² + 15R²) = 0.94

$\longrightarrow$  2(47R²) = 0.94

$\longrightarrow$  94R² = 0.94

$\longrightarrow$  R² = 0.01

$\longrightarrow$  R² = (0.1)²

$\longrightarrow$  R = 0.1

Dimensions of the closed cuboid are :

★  Length = (5 × 0.1) = 0.5 m

★  Breadth = (4 × 0.1) = 0.4 m

★  Height = (3 × 0.1) = 0.3 m