SURFACE AREA OF PYRAMIDS AND CONES WORKSHEET

About "Surface Area of Pyramids and Cones Worksheet"

Surface Area of Pyramids and Cones Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on surface area of pyramids and cones.

Before look at the worksheet, if you would like to know the basic stuff about surface area of pyramids and cones,

Surface Area of Pyramids and Cones Worksheet - Problems

Problem 1 :

Find the surface area of the regular pyramid shown below.

Problem 2 :

The lateral faces of the Pyramid Arena in Memphis, Tennessee, are covered with steel panels. Use the diagram of the arena shown below to find the area of each lateral face of this regular pyramid.

Problem 3 :

Find the surface area of the regular pyramid shown below.

Problem 4 :

Find the surface area of the right cone shown below.

Problem 5 :

The surface area of a right cone is 30π square inches and the slant height is 7 inches. Find the radius of the base of the cone.

Surface Area of Prisms and Cylinders Worksheet - Solutions

Problem 1 :

Find the surface area of the regular pyramid shown below.

Solution :

The base is a square.

Use the formula for the area of a square to find the area of the base,

B  =  side ⋅ side

B  =  2 ⋅ 2

B  =  4 cm2

The perimeter of the base is

P  =  4 ⋅ side

P  =  4 ⋅ 2

P  =  8 cm

The slant height is

l  =  √2 cm

Formula surface area of a right pyramid is

S  =  B + 1/2 ⋅ Pl

Substitute 4 for the area of the base B, 8 for P and √2 for l.

S  =  4 + 1/2 ⋅ (8)(√2)

Simplify.

S  =  4 + 4√2

Use calculator.

S  ≈  9.7

So, the surface area of the regular pyramid is about 9.7 square cm.

Problem 2 :

The lateral faces of the Pyramid Arena in Memphis, Tennessee, are covered with steel panels. Use the diagram of the arena shown below to find the area of each lateral face of this regular pyramid.

Solution :

To find the slant height of the pyramid, use the Pythagorean Theorem in the right triangle triangle shown below.

(Slant height)2  =  h2 + (1/2 ⋅ s)2

Substitute.

(Slant height)2  =  3212 + 1502

Simplify.

(Slant height)2  =  103,041 + 22,500

(Slant height)2  =  103,041 + 22,500

(Slant height)2  =  125,541

Take square root on both sides.

(Slant height)2  =  125,541

Use calculator.

Slant height  ≈  354.32

The area of each lateral face is

=  1/2 ⋅ (base area of lateral face)(slant height)

Substitute.

1/2 ⋅ (300)(354.32)

≈  53,148

So, the area of each lateral face is about 53,148 square feet.

Problem 3 :

Find the surface area of the regular pyramid shown below.

Solution :

To find the surface area of the regular pyramid shown, start by finding the area of the base.

A diagram of the base is shown below.

The base is a regular hexagon.

Use the formula for the area of a regular polygon to find the area of the base,

=  1/2 ⋅ (apothem)(perimeter)

Substitute.

=  1/2 ⋅ (3√3)(6 ⋅ 6)

Simplify.

=  54√3 square meters

Formula for area of a regular pyramid is

S  =  B + 1/2 ⋅ Pl

Substitute 54√3 for the area of the base B, 36 for P and 8 for l.

S  =  54√3 + 1/2 ⋅ (36)(8)

Simplify.

S  =  54√3 + 144

Use calculator.

S  ≈  237.5

So, the surface area of the regular pyramid is about 237.5 square meters.

Problem 4 :

Find the surface area of the right cone shown below.

Solution :

Formula for surface area of a right cone is

S  =  πr+ πrl

Substitute.

S  =  π(42) + π(4)(6)

Simplify.

S  =  16π + 24π

S  =  40π

Use calculator.

S    125.7

So, the surface area of the right cone is about 125.7 square inches.

Problem 5 :

The surface area of a right cone is 30π square inches and the slant height is 7 inches. Find the radius of the base of the cone.

Solution :

Formula for surface area of a right cone is

S  =  πr+ πrl

Substitute.

30π  =  πr+ πr(7)

Factor.

30π  =  π(r+ 7r)

Divide each side by π.

30  =  r+ 7r

Subtract 30 from each side.

0  =  r+ 7r - 30

or

r+ 7r - 30  =  0

Solve the above quadratic equation using factoring

(r - 3)(r + 7)  =  0

r - 3  =  0     or     r + 7  =  0

r  =  3     or     r  =  -7

Radius can not be negative. Then, r  =  3.

So, the radius of the base of the cone is 3 inches.

After having gone through the stuff given above, we hope that the students would have understood, "Surface Area of Pyramids and Cones Worksheet".

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

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6