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13.	The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accommodate?
	A.  2 metres
	B.  3 metres
	C.  4 metres
	D.  3√3metres

Solution

Required length = Diagonal ‹=›√3 a ‹=›(√3×√3) m ‹=›3 m.

14.	An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
	A.  10 cm, 50 cm
	B.  20 cm, 100 cm
	C.  40 cm, 200 cm
	D.  None of these

Solution

Let the sides of the sheet be x and 5x. Then,volume of the sheet= volume of the cube ‹=› x × 5x ×1/2 ‹=› 10×10×10 ‹=› 5x2= 2000 ‹=› x2= 400 ‹=› x = 20. The sides are 20 cm and 100 cm.

15.	The perimeter of one face a of cube is 20 cm. Its volume must be
	A.  125 cm3
	B.  400 cm3
	C.  1000 cm3
	D.  8000 cm3

Solution

Edge of the cube = (20 / 4) cm ‹=›5 cm. Volume = (5×5×5)cm3 ‹=›125 cm3.