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Algebra Worksheets - Page 4

Algebra Worksheets
  • Page 4
 31.  
The formula for the volume of a rectangular pyramid is V = (1 3)lwh. Select a formula that would help you to find the height (h) of the pyramid.
a.
3Vl units
b.
Vlw units
c.
3Vw units
d.
3Vlw units


Solution:

V = (13) × lwh
[Formula.]

3V = (13) × lwh × (3)
[Multiply by 3 on each side.]

3V = lwh
[Simplify.]

3Vlw = lwhlw
[Divide each side by lw.]

3Vlw = h
[Simplify.]

So, the height of the rectangular pyramid is 3Vlw units.


Correct answer : (4)
 32.  
The formula F = 9 5C + 32 is used to convert temperature from Celsius (C) scale to Fahrenheit (F) scale. Which of the following choices best suits the conversion of temperature from Fahrenheit scale to Celsius scale?
a.
C = 5 9(F - 12)
b.
C = 5 9(F + 32)
c.
C = 5 9(F - 22)
d.
C = 5 9(F - 32)


Solution:

F = 95C + 32
[Formula.]

F - 32 = (95) × C + 32 - 32
[Subtract 32 from each side.]

F - 32 = (95) × C
[Simplify.]

5(F - 32) = 5 × (95) × C
[Multiply by 5 on each side.]

5(F - 32) = 9C
[Simplify.]

59(F - 32) = 9C9
[Divide by 9 on each side.]

59(F - 32) = C
[Simplify.]

The formula C = 5 / 9(F - 32) is used to convert temperature from Fahrenheit scale to Celsius scale.


Correct answer : (4)
 33.  
The formula S = n(n+1)2 is used to find the sum of the first n natural numbers. Find the sum of the first 14 natural numbers.
a.
105
b.
112
c.
98
d.
119


Solution:

S = n(n+1)2
[Formula.]

S = 14(14+1)2
[Replace n with 14.]

S = 14(15)2
[Add.]

S = 7(15)
[Divide.]

S = 105
[Multiply.]

The sum of the first 14 natural numbers is 105.


Correct answer : (1)
 34.  
Total surface area of a cube is given by the formula, L = 6s2, where s is the side of the cube. Find the side of the cube, if the total surface area of the cube is known.
a.
6L
b.
L6
c.
L2
d.
2L


Solution:

L = 6s2

L / 6 = s2
[Divide both sides by 6.]

L6 = s2
[Take square root on both sides.]

L6 = s

So, the side of the cube = L6


Correct answer : (2)
 35.  
Find the base of a triangle, if area of the triangle A and height h are known.
a.
h2A
b.
2hA
c.
2Ah
d.
2Ah


Solution:

Area of the triangle with base b and height h is A = 1 / 2 × bh.

2A = bh
[Multiply by 2 on both sides.]

2Ah = b
[Divide both sides by h.]

So, the base of the triangle is 2Ah.


Correct answer : (3)

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