Question

The total surface area of a cuboid is
194 m². If its length is 8 m and
breadth is 6 m, then what is its volume
(in m?)?
(1) 168
(2) 224
(3) 112
(4) 126​

Answer 1

Answer:-

V = 168 m³.

Option (1) is correct.

Given:-

Total surface area of cuboid = 194 m²

Length = 8 m

Breadth = 6 m

To find :-

Volume of the cuboid.

Solution :-

For, finding its volume first we have to find its height.

The total surface area of cuboid is given by :-

★ $\boxed{\sf{TSA = 2(lb + bh + lh)}}$

Put the given value,

→$194 = 2( 8 \times 6 + 6 \times h + 8 \times h)$

→$194 = 2 ( 48 + 6h + 8h )$

→$194 = 2 ( 48 + 14h )$

→$194 = 96 + 28h$

→$28h = 194 - 96$

→$28h = 98$

→$h = \dfrac{98}{28}$

→$h = 3.5 m$

Now, we have

h = 3.5 m

l = 8 m

b = 6 m

Volume of cuboid is given by :-

★ $\boxed{\sf{ V = lbh}}$

→$V = 8 \times 6 \times \ 3.5$

→$V = 168 m^3$

hence,

The volume of cuboid is 168 m³.

Answer 2

Answer:

Volume of the cuboid = 168 m³

Step-by-step explanation:

given that,

The total surface area of a cuboid is

194 m².

we know that,

total surface area of a cuboid

= 2lb + 2bh + 2lh

where,

l = length of the cuboid

b = breadth of it

h = height of the cuboid

also,

given that,

its length is 8 m and

breadth is 6 m

here,

length = 8 m

breadth = 6 m

putting the values,

194 = 2[8(6) + 6(h) + 8(h)]

48 + 6h + 8h = 194/2

14h = 97 - 48

14h = 49

h = 49/14

h = 7/2

h = 3.5 m

so,

height of the cuboid = 3.5 m

now,

volume of the cuboid

we know that volume of a cuboid

= length × breadth × height

putting the values,

volume = 8m × 6m × 3.5m

= 168 m³

so,

Volume of the cuboid

= 168 m³