Question

Solve the formula for the indicated variable. Then
evaluate the rewritten formula for the given values. Use 3.14 for Π.

1)  Area: A = (1/2)bh  

Solve for b. Find the value of b.  When A=160 and h=20

2)  Volume:V = (1/3)Πr²h  

Solve for h. Find the value of h.  When V=84 and r=4.

3)  Volume: V = Πr²h  

Solve for h. Find the value of h.  When V=790 and r=5.

Answer 1

1) Area: A = (1/2)bh

A=160 and h=20

These values are substitute in above formula

160= (1/2)b(20)

Divide each side by 20

160/20=(20/2*20)b                               (Divide:160/20=8)

8 = (1/2)b

Multiply each side by 2

8*2 = (2/2)b                                        (Multiply:8 * 2 = 16)

b = 16

The value of b is 16.

2)Volume:V = (1/3)Πr²h  

Solve for h. Find the value of h

When V=84 and r=4.

Given volume   V = (1/3)Πr²h   

given v =84 and r =4 and Π =3.14

Substitute value in above formula,then

84 = (1/3)3.14×4² h                       ( 4²=16)

84=   (3.14/3)16 Ã—h                       (3.14/3 =1.46)

84 = (1.46)16 Ã—h                           (1.46×16=23.36 )

84 = 23.36 Ã—h                               ( Divide each side by 23.36)

84/23.36 = 23.36/23.36×h

3.59   = h                                         (84/23.36=3.59)

h =3.59

The value of h =3.59.

3)Volume: V = Πr²h  

 Solve for h. Find the value of h

 When V=790 and r=5.

Given volume   V = Πr²h   

given v = 790 and r =5 and Π =3.14

Substitute value in above formula,then

790 = 3.14×5² h                                   (Substitute:v = 790, r = 5, and Π =3.14)

790 =   3.14×25 Ã—h                           (Multiply: 5²=5×5 = 25)

790 =   78.5×h                                     (Multiply: 3.14×25=78.5)

790/78.5=   78.5/78.5×h                       (Divide each side by 78.5)

10.06=   h                                              (Divide: 790/78.5 = 10.06, and 78.5/78.5 = 1)

h =10.06

The value of h =10.06.

Comments

2).

Volume : V = (1/3)Πr²h.

Solve for h :

h = (3V)/Πr² .

Substitute the values V = 84, Π = 3.14, and r = 4.

h = (3 * 84)/(3.14 * 4 * 4)

= (3 * 21)/(3.14 * 4)

= 63/12.56

= 5.0159.

Therefore, h = 5.015.

3).

h = V/Πr².

= 790 / (3.14 * 5 * 5)

= 158 / (3.14 * 5)

= 158 / (15.7)

= 10.06.

Therefore, h = 10.06.