Question

If the cube shown has a volume of 1,000 cm3, what is the length of the diagonal, x, of the cube? (rounded to the nearest tenth)
A) 16.6 cm
B) 16.9 cm
C) 17.3 cm
D) 17.8 cm

Answer 1

Answer: 17.3 cm

Step-by-step explanation:Since, s3 = 1,000 → s =  

1,000

→ s = 10.

If

y2 = 102 + 102 → y =  

100 + 100

=  

200

then,

x2 = 102 + (

200

)2 → x =  

100 + 200

=  

300

≈ 17.32

Answer 2

C) 17.3 cm

The length of the diagonal, x, of the cube is  17.3 cm.

Explanation:

Given : The volume of the cube = 1,000 cm³

Since Volume of cube = (side)³

⇒ (side)³= 1000

Taking cube root on both sides , we get

side =10 cm

Also, the length of the diagonal in a cube = $\sqrt{3}(side)$

So , the length of the diagonal in given cube =$\sqrt{3}(10)$

$(1.73)(10)$  [$\sqrt{3}=1.73$ ]

$=17.3\ cm$

Hence, the length of the diagonal, x, of the cube is 17.3 cm.

Thus , the correct answer is C) 17.3 cm .

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