## PROBLEMS ON VOLUME

To find volume of the shapes, we will be using the formulas given below.

Volume of sphere  =   (4/3) π r3

Volume of hemisphere  =   (2/3) π r3

Volume of cone  =   (1/3) π r2h

Volume of cylinder  =   π r2h

Problem 1 :

A steel bar is 2.2 m long and has a diameter of 5 cm. Find the volume of the bar in cm3.

Solution :

Length of steel bar  =  2.2 m  (or)  220 cm

Radius  =  5/2  ==>  2.5 cm

Volume of steel bar  =  π r2h

=  (3.14) (2.5)2(220)

=  4317.5 cm3

Problem 2 :

A stainless steel wine vat is cylindrical with base diameter 1.8 m and height 6 m. How much wine does it hold if it is 90% full?

Solution :

Radius  =  1.8 m, height  =  6 m

Volume of steel bar  =  90% of π r2h

=  0.90 x 3.14 x (1.8)2 x 6

=  54.93 m3

Problem 3 :

A box has a square base and its height is 12 cm. If the volume of the box is 867 cm3, find its length.

Solution :

Let base length of the square as x.

Volume of box  =  867 cm3

Area of square base x height  =  867

x2 x 12  =  867

x2  =  867/12

x2  =  72.25

x  =  8.5 cm

Problem 4 :

15.4 mm of a rain falls on a rectangular shed roof of length 12 m and width 5.5 m. All of the water goes into a cylindrical tank of base diameter 4.35 m. By how much does the water level in the tank rise in mm ?

Solution :

Measures of rectangular shed :

Length  =  12 m  =  12000 mm

width  =  5.5 m  =  5500  mm

height  =  15.4 mm

Radius  =  4.35/2  =  2.175 m

=  2175 mm

Volume of water in rectangular tank  =  Volume of water in cylindrical tank

length x width x height  =  π r2h

12000 x 5500 x 15.4  =  3.14 x (2.175)2 x h

h  =  (12000 x 5500 x 15.4)/3.14 x (2175)2

h  =  68.42 mm

Problem 5 :

Find the volume of the figure shown below.

Solution :

Volume  =  Base area x height

Base area  =  Area of large circle - Area of small circle

Let R and r be radius of large and small circles respectively.

R  =  0.8/2, r  =  0.4/2

R  =  0.4 m and r  =  0.2 m

Area of base  =  πR2 -  πr2

=   π(0.42 - 0.22)

=  3.14(0.12)

Area of base  =  0.3768 m2

Height  =  1.2 m

Volume  =  0.3768 x 1.2

=  0.45216 m3

Problem 6 :

Find the volume of the figure given below.

Solution :

Volume of cylinder  =  πr2h

radius  =  6 cm and height  =  10 cm

=  π(6)2 (10)

=  3.14(36)(10)

Volume of cylinder  =  1130.4 cm3

Problem 7 :

Tom has just had a load of sand delivered. A pile of sand is in the shape of a cone of radius 1.6 m and height 1.2 m. Find the volume of sand Tom has had delivered.

Solution :

Volume of sand to be delivered  =  (1/3) πr2h

radius  =  1.6 m and height  =  1.2 m

=  (1/3) π(1.6)2(1.2)

=  (1/3)x3.14x(1.6)2(1.2)

=  3.19 m3

Volume of sand delivered is 3.19 m3.

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

Kindly mail your feedback to v4formath@gmail.com

WORD PROBLEMS

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

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

## Recent Articles

1. ### Linear Growth and Decay

May 22, 22 03:05 AM

Linear Growth and Decay

2. ### Worksheet on Probability

May 22, 22 01:15 AM

Worksheet on Probability