Volume of Cuboid

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


Formula for finding the volume of a cuboid

Volume of a Cuboid (V) = l × b × h;

Where l = Length, b = breadth and h = height.


1. A field is 15 m long and 12 m broad. At one corner of this field a rectangular well of dimensions 8 m × 2.5 m × 2 m is dug, and the dug-out soil is spread evenly over the rest of the field. Find the rise in the level of the rest of the field.

Solution:

Formula for Finding the Volume of a Cuboid

The volume of soil removed = The Volume of the Well

                                         = 8 m × 2.5 m × 2 m

                                         = 8 × 2.5 × 2 m3

                                         = 40 m3


Let the level of the rest of the field be raised by h.

Volume of the Cuboid of Dimensions

The volume of the soil spread evenly on the field

                            = Volume of the cuboid of dimensions + Volume of the cuboid of dimensions

                            = 2.5 m × 4 m × h + 12.5 m × 12 m × h

                            = (2.5 m × 4 m × h + 12.5 m × 12 m × h)

                            = (10h + 150h) m\(^{2}\)

                            = 160h m\(^{2}\)

Therefore, 160h m\(^{2}\) = 40 m3

⟹ h = \(\frac{40}{160}\) m

⟹ h = \(\frac{1}{4}\) m

Therefore, the rise in the level = \(\frac{1}{4}\) m

                                            = 25 cm


2. Squares each side 8 cm are cut off from the four corners of a sheet of tin measuring 48 cm by 36 cm. The remaining portion of the sheet is folded to form a tank open at the top. What will be the capacity of the tank?

Solution:

To make the tank, NGHP has to folded up along NP, LMQK along MQ, EFNM along MN and IJQP.

Capacity of the Tank
The Capacity of the Tank

Now, MN = QP = (48 - 2 × 8) cm = 32 cm, and

NP = MQ = (36 - 2 × 8) cm = 20 cm.

EM = KQ = IP = GN = 8 cm.

Therefore, the capacity of the tank = 32 × 20 × 8 cm3

                                                   = 5120 cm3

                                                   = 5.12 litres [Since, 1 litre = 1000 cm3]





9th Grade Math

From Volume of Cuboid 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. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 18, 24 02:59 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

    May 12, 24 06:28 PM

    Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

    Read More

  3. Face Value and Place Value|Difference Between Place Value & Face Value

    May 12, 24 06:23 PM

    Face Value and Place Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More

  4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    May 12, 24 06:09 PM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  5. Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

    May 12, 24 04:59 PM

    Bar Graph Worksheet
    In math worksheet on bar graphs students can practice the questions on how to make and read bar graphs or column graphs. Test your knowledge by practicing this graphing worksheet where we will

    Read More