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Pythagorean Theorem in Three Dimensions Worksheet



Downside 1 : 

A field used for delivery slender silver sticks measures 6 inches by 6 inches by 20 inches. What is the size of the longest stick that may match within the field, on condition that the size of the tube have to be a entire variety of inches ?

Downside 2 : 

Lily ordered a alternative half for her desk. It was shipped in a field that measures 4 in. by 4 in. by 14 in. What’s the best size in entire inches that the half might have been ?

Solutions

1. Reply :

Step 1 : 

Draw an acceptable diagram for the given data.

From the diagram given above, the field has the next dimensions.

Size (l)  =  20 in.

Width (w)  =  6 in.

Top (h)  =  6 in.

Step 2 :

We need to discover d, the size from a backside nook to the reverse prime nook. First, discover s, the size of the diagonal throughout the underside of the field.

w2 + l2  =  s2

Step 3 :

Substitute the given measures.

62 + 202  =  s2

Simplify.

36 + 400  =  s2

436  =  s2

Step 3 :

Use the expression for s to seek out d.

h2 + s2  =  d2

Step 4 :

Substitute h = 6 and s2 = 436. 

62 + 436  =  d2

Simplify.

36 + 436  =  d2

472  =  d2

Take sq. root on either side.

√472  =  √d2

21.7  ≈  d

Therefore, the size of the longest stick that may match within the field is 21 inches.

2. Reply :

Step 1 : 

Draw an acceptable diagram for the given data.

From the diagram given above, the field has the next dimensions.

Size (l)  =  14 in.

Width (w)  =  4 in.

Top (h)  =  4 in.

Step 2 :

We need to discover d, the size from a backside nook to the reverse prime nook. First, discover s, the size of the diagonal throughout the underside of the field.

w2 + l2  =  s2

Step 3 :

Substitute the given measures.

42 + 142  =  s2

Simplify.

16 + 196  =  s2

212  =  s2

Step 3 :

Use the expression for s to seek out d.

h2 + s2  =  d2

Step 4 :

Substitute h = 4 and s2 = 212. 

42 + 212  =  d2

Simplify.

16 + 212  =  d2

228  =  d2

Take sq. root on either side.

√228  =  √d2

15.1  ≈  d

Therefore, the best size that the half might have been 15 inches. 

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