Volume of Cube

Here we will learn how to solve the application problems on Volume of cube using the formula.

Formula for finding the volume of a cube

Volume of a Cube (V) = (edge)3 = a3;

where a = edge


1. A cubical wooden box of internal dimensions 1 m × 1 m × 1 m is made of 5 cm thick wood. The wood costs Rs. 18600 per cubic metre. If the box is open at the top, find the cost of wood required for making the box.


Volume of Cube Image

Clearly, the outer dimensions of the box are as follows

The outer length = 1 m + 2 × 5 cm = 1.10 m

The outer breadth = 1 m + 2 × 5 cm = 1.10 m

The outer height = Inner height + 5 cm (since, the box is open at the top)

                         = 1.05 m

Therefore, the volume of wood required = Volume of the outer cuboid - volume of the inner cube

                                                          = 1.10 × 1.10 × 1.05 m3 - 13m3

                                                          = 1.2705 m3 - 1 m3

                                                          = 0.2705 m3

Therefore, the cost of wood = 0.2705 × Rs. 18600

                                        = Rs. 5031.30

2. The edge of a cubical block of wood measures 30 cm. A straight cylindrical hole of diameter 10 cm is drilled through the cube. Find the volume of the wood left in the block.


Edge of a Cubical Block

Are of the cross section of the wood block left = Area of a face of the cube of edge 30 cm - Area of a circle of diameter 10 cm.

                                                                   = {302 - π ∙ (\(\frac{10}{2}\))2} cm2

                                                                   = (900 - 25π) cm2.

Cross Section of the Wood Block

Therefore, the volume of the wood left = (Are of the cross section) × Height

                                                         = (900 - 25π) × 30 cm3.

                                                         = (27000 - 750 × \(\frac{22}{7}\)) cm3.

                                                         = \(\frac{172500}{7}\) cm3.

                                                         = 24,642\(\frac{6}{7}\)cm3.

9th Grade Math

From Volume of Cube to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Jul 12, 24 03:08 PM

    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Worksheet on Fractions | Questions on Fractions | Representation | Ans

    Jul 12, 24 02:11 PM

    Worksheet on Fractions
    In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

    Read More

  3. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Jul 12, 24 03:21 AM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  4. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    Jul 12, 24 12:59 AM

    To convert an improper fraction into a mixed number, divide the numerator of the given improper fraction by its denominator. The quotient will represent the whole number and the remainder so obtained…

    Read More

  5. Conversion of Mixed Fractions into Improper Fractions |Solved Examples

    Jul 12, 24 12:30 AM

    Conversion of Mixed Fractions into Improper Fractions
    To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerat…

    Read More