# VOLUME OF PYRAMIDS AND CONES WORKSHEET

## About "Volume of Pyramids and Cones Worksheet"

Volume of Pyramids and Cones Worksheet :

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

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

## Volume of Pyramids and Cones Worksheet - Problems

Problem 1 :

Find the volume of the pyramid with the regular base. Problem 2 :

Find the volume of the right circular cone shown below. Problem 3 :

Find the volume of the oblique circular cone shown below. Problem 4 :

The volume of the right circular cone shown below is 2614 cubic feet. Find the value of x. Problem 5 :

A nautical prism is a solid piece of glass, as shown. Find its volume. Problem 6 :

If oil is being poured into the funnel shown below at a rate of 147 milliliters per second and flows out of the funnel at a rate of 42 milliliters per second, estimate the time it will take for the funnel to overflow. (1 mL  =  1 cm3)  ## Volume of Pyramids and Cones Worksheet - Solutions

Problem 1 :

Find the volume of the pyramid with the regular base. Solution :

The base can be divided into six equilateral triangles as shown below. Using the formula for the area of an equilateral triangle,

√3/4 ⋅ s2

the area of the base B can be found as follows :

B  =  6(√3/4 ⋅ s2)

Substitute 3 for s.

B  =  6(√3/4 ⋅ 32)

Simplify.

B  =  6(√3/4 ⋅ 9)

B  =  27√3 / 2  cm2

Formula for volume of a pyramid :

V  =  1/3 ⋅ Bh

Substitute 27√3 / 2 for B and 4 for h.

V  =  1/3 ⋅ (27√3 / 2)(4)

Simplify.

V  =  18√3

V  =  31.2

So, the volume of the pyramid is about 31.2 cubic centimeters.

Problem 2 :

Find the volume of the right circular cone shown below. Solution :

Formula for volume of a cone :

V  =  1/3 ⋅ πr2h

Substitute 12.4 for r and 17.7 for h.

V  =  1/3 ⋅ π(12.4)2(17.7)

Simplify.

V  =  907.184π

Use calculator.

V  ≈  2850 mm3

So, the volume of the right circular cone is about 2850 cubic millimeters.

Problem 3 :

Find the volume of the oblique circular cone shown below. Solution :

Formula for volume of a cone :

V  =  1/3 ⋅ πr2h

Substitute 1.5 for r and 4 for h.

V  =  1/3 ⋅ π(1.5)2(4)

Simplify.

V  =  3π

Use calculator.

V  ≈  9.42 in3

So, the volume of the oblique circular cone is about 9.42 cubic inches.

Problem 4 :

The volume of the right circular cone shown below is 2614 cubic feet. Find the value of x. Solution :

Formula for volume of a cone :

V  =  1/3 ⋅ πr2h

Substitute 2614 for V, x for r and 13 for h.

2614  =  1/3 ⋅ πx2(13)

Multiply each side by 3.

7842  =  13πx2

Divide each side by 13π.

7842/13π  =  x2

Find positive square root.

13.86  ≈  x

So, the value of x is about 13.86

Problem 5 :

A nautical prism is a solid piece of glass, as shown. Find its volume. Solution :

To find the volume of the entire solid, we have to add the volumes of the prism and the pyramid.

The bases of the prism and the pyramid are regular hexagons made up of six equilateral triangles.

To find the area of each base, B, multiply the area of one of the equilateral triangles by 6.

That is, 6(√3/4 ⋅ s2), where s is the base edge.

Let V1 be the volume of prism and V2 be the volume of pyramid.

Volume of Prism :

V1  =  Bh

V1  =  6(√3/4 ⋅ s2⋅ h

Substitute 3.25 for s and 1.5 for h.

V1  =  6[√3/4 ⋅ (3.25)2⋅ 1.5

Use calculator and simplify.

V1    41.166

Volume of Pyramid :

V2  =  1/3 ⋅ 6(√3/4 ⋅ s2⋅ h

Substitute 3 for s and 3 for h.

V2  =  1/3 ⋅ 6(√3/4 ⋅ 32⋅ 3

Use calculator and simplify.

V1    23.38

Volume of the Nautical Prism :

V  =  V1 + V2

V  ≈  41.16 + 23.38

V  ≈  64.54  in3

So, the volume of the nautical prism is about 64.54 cubic inches.

Problem 6 :

If oil is being poured into the funnel shown below at a rate of 147 milliliters per second and flows out of the funnel at a rate of 42 milliliters per second, estimate the time it will take for the funnel to overflow. (1 mL  =  1 cm3) Solution :

First, find the approximate volume of the funnel.

Because the funnel is in the shape of cone, we can use formula for volume of a cone to find volume of the funnel.

V  =  1/3 ⋅ πr2h

Substitute 5 for r and 8 for h.

V  =  1/3 ⋅ π(52)(8)

Simplify.

V  =  1/3 ⋅ π(25)(8)

V  =  200π/3

Use calculator.

V  ≈  209  cm3

Because, 1mL  =  1cm

V  ≈  209  mL

The rate of accumulation of oil in the funnel is

=  147 - 42

=  105 mL/s

To find the time it will take for the oil to fill the funnel, divide the volume of the funnel by the rate of accumulation of oil in the funnel as follows :

=  209 mL ÷ 105 mL/s

Simplify.

≈  2 seconds

So, the funnel will overflow after about 2 seconds. After having gone through the stuff given above, we hope that the students would have understood, "Volume 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 