**Problem 1 : **

Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.

**Problem 2 : **

Find the surface area of the right prism shown below.

**Problem 3 : **

Find the surface area of the right prism shown below.

**Problem 4 : **

Find the surface area of the right cylinder shown below.

**Problem 5 : **

Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.

**Problem 1 : **

Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.

**Solution : **

Draw a sketch.

The prism has 6 faces, two of each of the following :

The surface area of the prism is

S = 2(40) + 2(24) + 2(15)

S = 80 + 48 + 30

S = 158

So, the surface area of the right rectangular prism is 158 square inches.

**Problem 2 : **

Find the surface area of the right prism shown below.

**Solution : **

Each base measures 5 inches by 10 inches with an area of

B = 5(10)

B = 50 in^{2}

The perimeter of the base is

P = 30 in.

and the height is

h = 6 in.

The surface area is

S = 2B + Ph

S = 2(50) + 30(6)

S = 100 + 180

S = 280

So, the surface area of the right prism is 280 square inches.

**Problem 3 : **

Find the surface area of the right prism shown below.

**Solution : **

In the above prism, each base is an equilateral triangle with a side length s, of 7 meters as shown below.

Using the formula for the area of an equilateral triangle, the area of each base is

B = 1/4 ⋅ √3(s^{2})

B = 1/4 ⋅ √3(7^{2})

B = 1/4 ⋅ 49√3

B = 49√3 / 4 m^{2}

The perimeter of each base is

P = 21 m

and the height is

h = 5 m

The surface area is

S = 2B + Ph

S = 2(49√3/4) + 21(5)

S = 49√3/2 + 105

Use calculator.

S ≈ 147 m^{2}

So, the surface area of the right prism is about 147 square meters.

**Problem 4 : **

Find the surface area of the right cylinder shown below.

**Solution : **

Each base has a radius of 3 feet, and the cylinder has a height of 4 feet.

Formula for surface area of a cylinder :

S = 2πr^{2} + 2πrh

Substitute.

S = 2π(3)^{2} + 2π(3)(4)

S = 18π + 24π

S = 42π

Use calculator.

S ≈ 131.95

So, the surface area of the right cylinder is about 132 square meters.

**Problem 5 : **

Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.

**Solution : **

Draw a sketch.

Formula for surface area of a cylinder :

S = 2πr^{2} + 2πrh

Substitute.

592.19 = 2π(6.5)^{2} + 2π(6.5)(4)

592.19 = 84.5π + 13πh

Subtract 84.5π from each side.

592.19 - 84.5π = 13πh

Simplify.

326.73 ≈ 13πh

Divide each side by 13π.

326.73/13π ≈ h

Use calculator and simplify.

8 ≈ h

So, the height of the cylinder is about 8 cm.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**