Find the dimensions of the square?

Question

A block of lead is hammered out to form asquare sheet 10 mm thick. The original dimensions ofthe block were 1,6 dm x 0,7 dm x 0,2 dm. Find the dimensions of the square

Answer 1

The original block was 16 cm * 7 cm * 2 cm = 224 cubic cm.

10 mm thick = 1 cm thick.

So the surface of the square is 224 cubic cm / 1 cm = 224 square cm.

Take the square root of 224, and one side of the square is 14.967 cm. So the dimensions of the square are 14.967 cm x 14.967 cm.

Answer 2

The volume of the resulting rectangular solid is = to the side of the square squared times the thickness of 10 mm.
(s mm) X (s mm) X (10 mm) = 10s^2 cu mm

The volume of the original rectangular solid was
l(length) X w(width) X h(height).

Change all dimensions to mm first. This implies the original block is 160 mm by 70 mm by 20 mm
as 1 dm = 100 mm.

So we get original volume is 160(70)(20) = 224,000 cu mm

Setting the two volumes equal results in

10s^2 = 224,000 dividing both sides by 10 ==>
s^2 = 22,400 take the square root of both side of this equation
s = sqrt(22,400) = sqrt(1600)sqrt(14) = 40sqrt(14) mm

check you answer by showing:

[40sqrt(14)mm]^2 X 10 mm = 224,000 cumm
40^2 x [sqrt(14)]^2 sqmm x 10 mm = 224,000 cumm
1600 x 14 x 10 cumm = 224,000 cumm
224,000 cumm = 224,000 ccmm

Answer 3

Hi. Solve for the volume (1.6dm times 0.7dm times 0.2dm). This will be constant. Convert 10mm to dm. Assume the expansion s linear and multiply the original l,w,h to find the answer.

Answer 4

V=1.6*.7*.2 dm^3=.224dm^3=224cm^3

10mm=1cm thick
224cm^3/1cm=224cm^2
the square will be s=√224=4√14=14.97cm