Question
A rectangular water tank is open at the top. Its capacity is 24 m3. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the inner and outer surface of the tank at the rate of Rs. 10 per m2 is :
Answer: Option D
Depth of the tank :
$$\eqalign{
& = \left( {\frac{{24}}{{4 \times 3}}} \right)m \cr
& = 2\,m \cr} $$
Since the tank is open and thickness of material is to be ignored, we have
Sum of inner and outer surface :
$$\eqalign{
& = 2\left[ {\left\{ {2\left( {l + b} \right) \times h} \right\} + lb} \right] \cr
& = 2\left[ {\left\{ {2\left( {4 + 3} \right) \times 2} \right\} + 4 \times 3} \right]{m^2} \cr
& = 80\,{m^2} \cr} $$
∴ Cost of painting :
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {80 \times 10} \right) \cr
& = {\text{Rs}}{\text{. 800}} \cr} $$
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Depth of the tank :
$$\eqalign{
& = \left( {\frac{{24}}{{4 \times 3}}} \right)m \cr
& = 2\,m \cr} $$
Since the tank is open and thickness of material is to be ignored, we have
Sum of inner and outer surface :
$$\eqalign{
& = 2\left[ {\left\{ {2\left( {l + b} \right) \times h} \right\} + lb} \right] \cr
& = 2\left[ {\left\{ {2\left( {4 + 3} \right) \times 2} \right\} + 4 \times 3} \right]{m^2} \cr
& = 80\,{m^2} \cr} $$
∴ Cost of painting :
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {80 \times 10} \right) \cr
& = {\text{Rs}}{\text{. 800}} \cr} $$
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