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Volumes Practice Test 4

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Question : 10 of 16

Marks: +1, -0

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8

m^3

. Find the breadth of the wall.

25 cm
30 cm
35 cm
40 cm

Solution:

Concept:

The wall is a cuboid, so its volume is

V = l \times b \times h

.

Explanation:

Let the breadth be

b

.

Height is 5 times breadth, so

h = 5b

.

Thus,

b = \frac{h}{5}

.

Length is 8 times height, so

l = 8h

.

Volume:

V = l \times b \times h = 8h \times \frac{h}{5} \times h

.

So,

\frac{8h^3}{5} = 12.8

.

h^3 = \frac{12.8 \times 5}{8} = 8

.

Hence,

h = 2

m.

Breadth

= \frac{h}{5} = \frac{2}{5}

m.

Convert to cm:

\frac{2}{5} \times 100 = 40

cm.

Answer:

The breadth of the wall is

40

cm, so the correct option is D.

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