Question

A cuboidal room has dimensions 20m×10m×5m and a cubical room has diamensions 10m×10m×10m find the ratio of their total surface areas. please fast give my the accurate answer​

Answer 1

Answer:

If the cuboidal room has dimensions 20m × 10m × 5m and a cubical room has dimensions 10m × 10m × 10m, then the ratio of their total surface areas is 7:6.

Step-by-step explanation:

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

A cuboidal room has dimensions 20m × 10m × 5m

So, Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh)

= 2 [(20) (10) + (10) (5) + (20) (5)]

= 2 [200 + 50 + 100]

= 2[350]

Surface Area of a Cuboid (TSA) = = 700 sq. m.

A cuboidal room has dimensions 10m × 10m × 10m

So, Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh)

= 2 [(10) (10) + (10) (10) + (20) (10)]

= 2 [100 + 100 + 100]

= 2[300]

Surface Area of a Cuboid (TSA) = = 600 sq. m.

So, the ratio of their total surface areas = 700 : 600

the ratio of their total surface areas = 7 : 6

Answer 2

The ratio of their total surface areas is 7 : 6.

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Let's understand a few concepts:

To calculate the total surface area of a cuboid we will use the following formula:

$\boxed{\bold{Total\:surface \:area \:of\:a\:cuboid= 2 [lb + bh + hl] }}$

where

l → length of the cuboid

b → breadth of the cuboid

h → height of the cuboid

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Let's solve the given problem:

The dimensions of the first cuboidal room:

Length = 20 m

Breadth = 10 m

Height = 5 m

The dimensions of the second cuboidal room:

Length = 10 m

Breadth = 10 m

Height = 10 m

By using the above formula of the total surface area of the cuboid, we get

The ratio of the total surface areas of the first cuboidal room to the second cuboidal room is,

= $\frac{T.S.A. \:of\:the \:1st\:room}{T.S.A. \:of\:the \:2nd\:room}$

= $\frac{2\times [(20 \times 10) + (10 \times 5) + (5\times 20)]}{2\times [(10 \times 10) + (10 \times 10) + (10\times 10)}$

= $\frac{ 200 \:+\: 50\: +\: 100}{ 100\: +\: 100\: +\: 100}$

= $\frac{350}{300}$

= $\frac{35}{30}$

= $\frac{7}{6}$

= $\bold{7:6}$

Thus, the ratio of their total surface areas is 7 : 6.

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