﻿ Algebra Worksheets | Problems & Solutions

# Algebra Worksheets

Algebra Worksheets
• Page 1
1.
The volume of a sphere is given by the formula V = $\frac{4}{3}\pi {r}^{3}$. Find the radius of a sphere whose volume is $14\frac{1}{7}$ m3?
 a. 15 m b. 17 m c. 1.7 m d. 1.5 m

#### Solution:

V = 43πr3

3V / 4= πr3

3V4π = r3

r3 = 3V4π

r = 3V4π3
[Solve the formula for r.]

r = 3 × 14174 × 2273

r = 3 × 99 × 74 × 22 × 73

r = 2783

r =1.5

The radius of the sphere is 1.5 m.

2.
The kinetic energy, E, of a body moving with a velocity $v$ is given by the equation E = $\frac{1}{2}m{v}^{2}$, where $m$ is the mass of the body. Find the mass of a body moving with a velocity 40 m/s and having an energy of 3000 N.
 a. 4.05 kg b. 3.75 kg c. 3.65 kg d. 6.75 kg

#### Solution:

E = 12mv2

2E = mv2

2Ev2 = m
[Solve the equation for m.]

m = 2 × 300040 × 40
[Substitute: E = 3000, v = 40.]

m = 2×7540 = 3.75

The mass of the body is 3.75 kg.

3.
Solve the formula V = $\frac{1}{3}$$\pi$$r$2$h$ for the variable $h$. Indicate any restrictions on the values of the variables.
 a. $h$ = $\frac{3+{r}^{2}}{\pi V}$, V ≠ 0 b. $h$ = $\frac{2\pi rV}{3}$, $r$ ≠ 0 c. $h$ = $\frac{3V}{\pi {r}^{2}}$, $r$ ≠ 0 d. $h$ = $\frac{V}{3\pi {r}^{2}}$, $r$ ≠ 0

#### Solution:

V = 1 / 3πr2h

3V = πr2h
[Multiply both sides by 3.]

3Vπr2 = h
[Divide both sides by πr2.]

h = 3Vπr2
[Symmetry property.]

The solution is h = 3Vπr2, r ≠ 0
[If r = 0, denominator becomes zero. Division by zero is undefined.]

4.
Solve the formula $p$ = 2($l$ + $b$) for $b$.
 a. $b$ = $\frac{p}{2}$ + $l$ b. $b$ = $\frac{2}{p}$ c. $b$ = $\frac{2p}{l}$ d. $b$ = $\frac{p}{2}$ - $l$

#### Solution:

p = 2(l + b)

p2 = l + b
[Divide both sides by 2.]

p2 - l = b
[Subtract l from both sides.]

b = p2 - l
[Symmetry property.]

5.
Solve the formula $v$ = $u$ + $\mathrm{at}$ for $a$. Indicate any restrictions on the values of the variables.
 a. $a$ = , $t$ ≠ 0 b. $a$ = , $t$ ≠ 0 c. $a$ = ($v$ + $u$)$t$, $v$ ≠ 0 d. $a$ = $u$ + $\mathrm{vt}$, $t$ ≠ 0

#### Solution:

v = u + at

v - u = at
[Subtract u from both sides.]

v - ut = a
[Divide both sides by t.]

a = v - ut
[Symmetry property.]

The solution is a = v - ut, t ≠ 0
[The solution must exclude values of a variable that make the denominator zero.]

6.
Solve $\frac{1}{f}$ = $\frac{1}{u}$ + $\frac{1}{v}$ for $u$.
 a. $u$ = $\frac{f-v}{fv}$ b. $u$ = -$\frac{1}{f}$ - $\frac{1}{v}$ c. $u$ = $\frac{f+v}{fv}$ d. $u$ = $\frac{fv}{v-f}$

#### Solution:

1f = 1u + 1v

1f - 1v = 1u
[Subtract 1v from both sides.]

v-ffv = 1u
[Simplify.]

fvv-f = u

7.
Solve $s$ = 2π$r$($r$ + $h$) for $h$ and indicate any restrictions on the values of the variables.
 a. $h$ = 4$s$, $s$ ≠ 0 b. $h$ = , $r$ ≠ 0 c. $h$ = 2π$\mathrm{rs}$ d. $h$ = $\frac{s}{2\pi r}$ - $r$, $r$ ≠ 0

#### Solution:

s = 2πr(r + h)

s2πr = r + h
[Divide both sides by 2πr.]

s2πr - r = h
[Subtract r from both sides.]

h = s2πr - r, r ≠ 0
[Symmetry property.]

8.
Solve P = $\frac{100I}{RT}$ for I.
 a. I = $\frac{100}{PRT}$ b. I = 100PRT c. I = $\frac{PRT}{100}$ d. I = 100 + PRT

#### Solution:

P = 100I / RT

PRT = 100I
[Multiply RT on both sides.]

PRT100 = I
[Divide both sides by 100.]

I = PRT100
[Symmetry property.]

9.
Solve V = $\pi$($R$ - $s$)$h$ for $s$.
 a. $s$ = $R$ + $\frac{V}{\pi h}$ b. $s$ = c. $s$ = $R$ - $\frac{V}{\pi h}$ d. $s$ = $R$ - $\frac{{V}^{2}}{\pi {h}^{2}}$

#### Solution:

V = π(R - s)h

Vπh = R - s
[Divide both sides by πh.]

Vπh - R = - s
[Subtract R from both sides.]

R - Vπh = s
[Multiply both sides by -1.]

s = R - Vπh

10.
Solve $y$ = $\mathrm{mx}$ + $c$ for $m$.
 a. $m$ = $\frac{x}{c}$ + $y$ b. $m$ = $x$($y$ + $c$) c. $m$ = d. $m$ =

#### Solution:

y = mx + c

y - c = mx
[Subtract c from both sides.]

y - cx = m
[Divide both sides by x.]