Question

the side of a cubical box is 80cm.find total surface area and cost of painting outer surface at the rate of ₹0.25 per cm^2​

Answer 1

Answer:

$\textsf{The cost of painting is Rs. 9600.}$

Step-by-step explanation:

$\textsf{Side of the cubical box = 80 cm}$

$\textsf{Rate of painting = Rs. 0.25 per sq.cm}$

$\textsf{The TSA and cost of painting of box = ??}$

__________________

★ $\textsf{\underline{Total Surface Area of Cube :}}$

$\sf{\longrightarrow} \: 6a^{2}$

$\sf{\longrightarrow} \:6 \times 6400$

$\sf{\longrightarrow} \: 38400 \: {cm}^{2}$

$\textsf{Total surface area of cube = 38400 sq.cm}$

__________________

★ $\textsf{\underline{Cost of painting outer sides of box :}}$

$\sf{\longrightarrow} \:Total \: surface \: area \times Rate \: of \: painting$

$\sf{\longrightarrow} \: 38400 \times 0.25$

$\sf{\longrightarrow} \: 9600$

$\textsf{Cost of painting = Rs. 9600}$

$\textsf{Therefore, the cost of painting is Rs. 9600.}$

Answer 2

${\large{\pmb{\sf{\bigstar \:{\underline{Understanding \: the \: Question...}}}}}}$

★ This question says that we have to find out the total surface area of a box which is in the shape of a cube. And the cubical box side is 80 centimetres. And also we have to find out the cost of painting outer surface at the rate of Rupees 0.25 per centimetres sq. Let's do it!

${\large{\pmb{\sf{\bigstar \:{\underline{Given \: that...}}}}}}$

★ A cubical shape box is given.

★ Side of the box is 80 cm.

${\large{\pmb{\sf{\bigstar \:{\underline{To \: find...}}}}}}$

★ Total surface area of box

★ The cost of painting outer surface at the rate of Rupees 0.25 per centimetres sq.

${\large{\pmb{\sf{\bigstar \:{\underline{Solution...}}}}}}$

★ Total surface area of box = 38400 cm²

★ The cost of painting outer surface at the rate of Rupees 0.25 per centimetres sq. = 9600 Rupees

${\large{\pmb{\sf{\bigstar \:{\underline{Using \: concepts...}}}}}}$

★ Formula to find out the total surface area of a cube.

${\small{\underline{\boxed{\sf{\bull \: TSA \: of \: cube \: = 6a^{2}}}}}}$

★ Formula to find out the cost(according to the question)

${\small{\underline{\boxed{\sf{\bull \: Cost \: = TSA \times Rate \: of \: painting}}}}}$

${\large{\pmb{\sf{\bigstar \:{\underline{Where...}}}}}}$

★ TSA denotes total surface area

★ a denotes the side

${\large{\pmb{\sf{\bigstar \:{\underline{Full \; Solution...}}}}}}$

~ Firstly let us find the total surface area of the cubical box by using the formula! Let's do it!

${\small{\underline{\boxed{\sf{\bull TSA \: of \: cube \: = 6a^{2}}}}}} \\ \\ :\implies \sf TSA \: of \: cube \: = 6a^{2} \\ \\ :\implies \sf TSA \: of \: cubical \: box \: = 6a^{2} \\ \\ :\implies \sf TSA \: of \: cubical \: box \: = 6(80)^{2} \\ \\ :\implies \sf TSA \: of \: cubical \: box \: = 6 \times 80 \times 80 \\ \\ :\implies \sf TSA \: of \: cubical \: box \: = 480 \times 80 \\ \\ :\implies \sf TSA \: of \: cubical \: box \: = 38400 \: cm \: sq.$

${\frak{\underline{Henceforth, \: 38400 \: cm \: sq. \: is \: TSA \: of \: box}}}$

~ Now by using the given formula let us find the cost of painting the outer surface at the rate of Rupees 0.25 per centimetres sq.

${\small{\underline{\boxed{\sf{\bull Cost \: = TSA \times Rate \: of \: painting}}}}} \\ \\ :\implies \sf Cost \: = TSA \times Rate \: of \: painting \\ \\ :\implies \sf Cost \: = 38400 \times 0.25 \\ \\ :\implies \sf Cost \: = 9600 \: Rupees$

${\frak{\underline{Henceforth, \: Rupees \: 9600 \: is \: cost \: of \: painting}}}$

${\large{\pmb{\sf{\bigstar \:{\underline{Additional \; Knowledge...}}}}}}$

${\pmb{\sf{Some \: formulas...}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Diagonal \: of \: cube \: = \sqrt{l^{2} + b^{2} + h^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}$

${\pmb{\sf{Where...}}}$

${\sf{\leadsto TSA \: denotes \: total \: surface \: area}}$

${\sf{\leadsto LSA \: denotes \: lateral \: surface \: area}}$

${\sf{\leadsto l \: denotes \: length}}$

${\sf{\leadsto b \: denotes \: breadth}}$

${\sf{\leadsto h \: denotes \: height}}$