Find the volume of the cubical box whose surface area is 486 $c{m^2}$.
Last updated date: 19th Mar 2023
•
Total views: 306.3k
•
Views today: 3.85k
Answer
306.3k+ views
Hint: Here, we will first find the value of the edge with the given surface area and then the Volume of the cubical box can be calculated as ${a^3}$.
Given,
Surface area of cubical box is 486 $c{m^2}$ i.e.., $6{a^2} = 486$ where ‘a’ is the edge .Now let us find the value of the edge i.e..,
$
\Rightarrow 6{a^2} = 486 \\
\Rightarrow {a^2} = \frac{{486}}{6} \\
\Rightarrow {a^2} = 81 \\
\Rightarrow a = 9 \\
$
Hence, the obtained value of edge (a) is 9 cm. As we know that the volume of the cubical box is ${a^3}$.
Therefore, substituting the obtained value of ‘a’ we get
$ \Rightarrow {a^3} = {9^3} = 729{\text{ c}}{{\text{m}}^3}$
Hence, the volume of the cubical box is 729 ${\text{c}}{{\text{m}}^{\text{3}}}$.
Note: Since, all the sides of a cubical box are equal. The volume of the cube is calculated by multiplying the value of a side 3 times i.e.., V=side*side*side.
Given,
Surface area of cubical box is 486 $c{m^2}$ i.e.., $6{a^2} = 486$ where ‘a’ is the edge .Now let us find the value of the edge i.e..,
$
\Rightarrow 6{a^2} = 486 \\
\Rightarrow {a^2} = \frac{{486}}{6} \\
\Rightarrow {a^2} = 81 \\
\Rightarrow a = 9 \\
$
Hence, the obtained value of edge (a) is 9 cm. As we know that the volume of the cubical box is ${a^3}$.
Therefore, substituting the obtained value of ‘a’ we get
$ \Rightarrow {a^3} = {9^3} = 729{\text{ c}}{{\text{m}}^3}$
Hence, the volume of the cubical box is 729 ${\text{c}}{{\text{m}}^{\text{3}}}$.
Note: Since, all the sides of a cubical box are equal. The volume of the cube is calculated by multiplying the value of a side 3 times i.e.., V=side*side*side.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts
Write an application to the principal requesting five class 10 english CBSE

Tropic of Cancer passes through how many states? Name them.

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE

What is per capita income

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
