﻿ Algebra Worksheets - Page 4 | Problems & Solutions

# Algebra Worksheets - Page 4

Algebra Worksheets
• Page 4
31.
The formula for the volume of a rectangular pyramid is $V$ = ($\frac{1}{3}$)$l$$w$$h$. Select a formula that would help you to find the height ($h$) of the pyramid.
 a. $\frac{3V}{l}$ units b. $\frac{V}{lw}$ units c. $\frac{3V}{w}$ units d. $\frac{3V}{lw}$ 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.

32.
The formula F = $\frac{9}{5}$C + 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 = $\frac{5}{9}$(F - 12) b. C = $\frac{5}{9}$(F + 32) c. C = $\frac{5}{9}$(F - 22) d. C = $\frac{5}{9}$(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.

33.
The formula S = $\frac{n\left(n+1\right)}{2}$ 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

S = 7(15)
[Divide.]

S = 105
[Multiply.]

The sum of the first 14 natural numbers is 105.

34.
Total surface area of a cube is given by the formula, L = 6$s$2, 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. $\sqrt{6L}$ b. $\sqrt{\frac{L}{6}}$ c. $\sqrt{\frac{L}{2}}$ d. 2$\sqrt{L}$

#### 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

35.
Find the base of a triangle, if area of the triangle A and height $h$ are known.
 a. $\frac{h}{2A}$ b. $\frac{2h}{A}$ c. $\frac{2A}{h}$ d. 2A$h$

#### 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.