Question

one Side a cube box is O.6m. How much will it
cost to paint the outers surface of the box
at the rate 70Rs per sq.m.​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that length of one side of a cube box is 0.6 m. We have to find the cost to paint the outer surface of the box at the rate Rs. 70 per m².

In order to find the cost to paint the outer surface of the box at the rate Rs. 70 per m², we need to calculate the total surface area of the box as its outer surface has to be painted. After that, we'll multiply Rs. 70 with the area we'll to find our answer.

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

According to the given question, we can say that :

★ Total cost to paint = Cost to paint per m² × T.S.A of cube

$\underline{\pmb{ \sf {\maltese \; \; \; Finding \: T.S.A_{(Cube)} \: : \; \; \; } }}$

We know that,

$\bigstar \: \boxed{\sf {T.S.A_{(Cube)}= 6 \ell^2}}$

$\longrightarrow \sf {T.S.A_{(Cube)}= 6 \times (0.6)^2 \: m^2}$

$\longrightarrow \sf {T.S.A_{(Cube)}= 6 \times {\Bigg ( \dfrac{6}{10} \Bigg )}^{2 }\: m^2}$

$\longrightarrow \sf {T.S.A_{(Cube)}= 6 \times \dfrac{6 \times 6}{10 \times 10}\: m^2}$

$\longrightarrow \sf {T.S.A_{(Cube)}= 6 \times \dfrac{36}{100}\: m^2}$

$\longrightarrow \sf {T.S.A_{(Cube)}= \dfrac{6 \times 36}{100}\: m^2}$

$\longrightarrow \sf {T.S.A_{(Cube)}= \dfrac{216}{100} \: m^2}$

$\longrightarrow \sf \red {T.S.A_{(Cube)}= 2.16 \: m^2}$

$\underline{\pmb{ \sf {\maltese \; \; \; Finding \: Total \: cost_{(to \: paint)} \: : \; \; \; } }}$

We are given that cost to paint per m² is Rs. 70. So, cost to paint 2.16 m² :

★ Total cost to paint = Cost to paint per m² × T.S.A of cube

$\longrightarrow \sf{Total \: cost_{(to \: paint)} = Rs. (2.16 \times 70) }$

$\longrightarrow \sf \red{Total \: cost_{(to \: paint)} = Rs. \: 151.2}$

Therefore, the cost to paint the outer surface of the box at the rate Rs. 70 per m² is Rs. 151.2.

________________

Answer 2

$\underline{\green{\sf{Given}}}$

• Side of Cube=0.6m
• The outers surface of the box
• at the rate Rs. 70 per m²

$\underline{\green{\sf{To ~ Find}}}$

• How much will it cost to paint the outers surface of the box at the rate 70Rs per sq.m.

$\underline{\green{\sf{Solution}}}$

$\implies\text{Surface area of Cube = 6a²}$

$\implies\text{Surface area of Cube = 6(0.6m)²}$

$\implies\text{Surface area of Cube = 6 ×\: 0.36 m²}$

$\implies\text{Surface area of Cube =2.16m²}$

Cost of the outers surface of the box at the rate 70Rs per sq.m.

$\text{Total cost to paint = Cost to paint per m² × T.S.A of cube}$

$\text{Total cost to paint = Cost to paint per m² × Surface Area of cube}$

$\text{Total cost to paint = Rs.70×2.16m²}$

$\text{Total cost to paint =\bf{ \green{Rs.151.2}}}$

• Rs.151.2 will it cost to paint the outers surface of the box at the rate Rs.70per m².