Volume and Surface Area of Cube and Cuboid

Here we will learn how to solve the problems on Volume and Surface Area of Cube and Cuboid:

1. Two cubes of edge 14 cm each are joined end to end to form a cuboid. Find the volume and the total surface area of the cuboid.


Volume and Surface Area of Cube and Cuboid

The volume of the cuboid = 2 × volume of one cube

                                     = 2 × 14\(^{3}\) cm\(^{3}\)

                                     = 5488 cm\(^{3}\)

The total surface area of the cuboid = 2(28 × 14 + 14 × 14 + 14 × 28) cm\(^{2}\)                                             

                                                    = 2(28 + 14 + 28) × 14 cm\(^{2}\)

                                                    = 2(2 × 14 + 1 × 14 + 2 × 14) × 14 cm\(^{2}\)

                                                    = 2(2 + 1 + 2) × 14 × 14 cm\(^{2}\)

                                                    = 2(5) × 14 × 14 cm\(^{2}\)

                                                    = 10× 14 × 14 cm\(^{2}\)

                                                    = 1960 cm\(^{2}\)

2. The dimensions of the base of a rectangular vessel are 60 cm × 45 cm. Its height is 20 cm. The vessel is half-filled with water. What should be the size of a solid iron cube which when dropped into the vessel will raise the water level up to the brim?


Application Problems on Volume and Surface Area of Cube and Cuboid

The volume of the vessel = 60 × 45 × 20 cm\(^{3}\)          

                                     = 54000 cm(^{3}\)  

It is half-filled with water      

So, the volume of the empty portion of the vessel = \(\frac{1}{2}\) × 54000 cm\(^{3}\)                                                                       

                                                                        = 27000 cm\(^{3}\) 

The volume of the iron cube should be 27000 cm\(^{3}\) so that it displaces this amount of water and the water level comes up to the brim.

If the edge of the cube is x then,

x\(^{3}\) = 27000 cm\(^{3}\)                                            

⟹ x\(^{3}\) = (30)\(^{3}\) cm\(^{3}\)

⟹ x = 30 cm

Therefore, the edge of the iron cube = 30 cm

The size of the cube should be 30 cm × 30 cm × 30 cm.

9th Grade Math

From Volume and Surface Area of Cube and Cuboid to HOME PAGE

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.

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.

Share this page: What’s this?

Recent Articles

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

    Mar 02, 24 05:31 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. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More