Question

The Area of a courtyard is 3750m². Find the cost of covering it with gravel to a height of 1 cm if the gravel costs $6.40 per cubic metre.

Answer 1

$\underline{\underline{\sf{ \pink{Given :} }}}$

• Area of courtyard = 3750 m²
• Height of gravel = 1 cm = 0.01 m
• Cost of gravel per cubic metre = $ 6.40

$\underline{\underline{\sf{ \pink{To\:Find :} }}}$

• Cost of gravel to cover the courtyard

$\underline{\underline{\sf{ \pink{Solution :} }}}$

$\underline{\tt{As\:we\:know\:that,}}$

$\star\:{\boxed{\sf{\pink{Volume = Base \: Area \times Height}}}}$

$: \: \implies \sf{Volume = 3750 \: m^{2} \times 0.01 \: m }$

$: \: \implies \sf{Volume = \Bigg(3750 \times \dfrac{1}{100}\Bigg) \: {m}^{3} }$

$: \: \implies \sf{Volume = \Bigg(375\cancel{0} \times \dfrac{1}{10\cancel{0}}\Bigg) \: {m}^{3} }$

$: \: \implies \sf{Volume = \dfrac{375}{10} \: {m}^{3} }$

$: \: \implies \sf{Volume = 37.5 \: {m}^{3} }$

_________________________

$\underline{\tt{We\:are\:given,}}$

Cost of 1 m³ = $ 6.40

$: \: \implies \sf{Total \: Cost \: of \: gravel = 37.5 \times \ 6.40 }$

$: \: \implies \sf{Total \: Cost \: of \: gravel = \dfrac{375}{10} \times \ \dfrac{64\cancel{0}}{10\cancel{0}}}$

$: \: \implies \sf{Total \: Cost \: of \: gravel = \dfrac{375}{10} \times \ \dfrac{64}{10}}$

$: \: \implies \sf{Total \: Cost \: of \: gravel = \ \dfrac{240\cancel{00}}{1\cancel{00}}}$

$: \: \implies \sf{Total \: Cost \: of \: gravel = \ 240}$

$\pink{\sf \therefore \: Total \: cost \: of \: covering \: the \: courtyard} \\ \pink{\sf with \: gravel \: of \: 1 \: cm \: height \: = \ 240}$