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)(b₁+b₂)

Solve for b₁. Find the value of b₁.  When A=30,b₂=8 and h=5.

2)  Surface Area: S =Πr²+Πrl

Solve for l. Find the value of l.  When S=100 and r=5

Answer 1

1)Area: A = (1/2)(b₁+b₂)

 Solve for b₁. Find the value of b₁

 When A=30,b₂=8 and h=5

Solution: Area: A = (1/2)(b₁+b₂)

A=30, h=5, b₂=8

These values are substitute in above formula

Area: 30 = (1/2)(b₁+8)

Multiply each side by 2

30×2=(1/2)(b₁+8)×2                             

60=(1)(b₁+8)                             (Multiply: 30×2 = 60, (1/2)×2 = 1)

b₁+8 = 60                                 (Multiply:(1)(b₁+8) =b₁+8 )

b₁+8 - 8= 60 - 8                        (Subtract 8 to each side)

b₁ = 52                                    (Subtract: 8 - 8 = 0, and 60-8 = 52)

The value of b₁ =52.

2)Surface Area: S =Πr²+Πrl

 Solve for l. Find the value of l

When S=100 and r=5

Given volume   S = Πr² + Πrl

given s = 100 and r =5 and Π =3.14

Substitute value in above formula,then

100 = (3.14)×5² + (3.14)×5×l       (Substitute:S = 100, r = 5, and Π =3.14)

100 =   3.14×25 +(3.14)×5×l        (Multiply: 5²=5×5 = 25)

100 =   78.5 +15.7×l                          (Multiply: 3.14×25=78.5, and (3.14)×5 = 15.7)

100 -78.5=78.5 +15.7×l -78.5             (Subtract 78.5 to each side)

21.5=15.7×l                                      (Simplify)

21.5/15.7 =15.7×l/15.7                      (Divide each side by 15.7)

1.369 = l                                             (Simplify)

The value of   l = 1.369.