Math, asked by Anonymous, 1 month ago

Good Evening !

A circle field of diameter 42 m needs to be cleaned. if the cost of cleaning the field is Rs. 2.35 per m², find the cost of cleaning the field?​

Answers

Answered by HolyGirl
2

 {\orange{\bigstar}} \ {\underline{\green{\textsf{\textbf{Given :-}}}}}

Diameter of the circle = 42 m

Cost of cleaning per m² = ₹2.35

 {\blue{\bigstar}} \ {\underline{\pink{\textsf{\textbf{To Find :-}}}}}

Cost of cleaning the whole field

 {\red{\bigstar}} \ {\underline{\purple{\textsf{\textbf{Formula Used :-}}}}}

 {\boxed{\green{\textsf{\textbf{Area of a circle = }}} {\blue{\sf{\pi r^2}}}}}

where,

r = Radius

 {\sf{\pi = \dfrac{22}{7}}}

 {\orange{\bigstar}} \ {\underline{\blue{\textsf{\textbf{Solution :-}}}}}

 Radius = {\sf{\dfrac{Diameter}{2}}}

 \longmapsto {\sf{\dfrac{42}{2}}}

 \longmapsto {\sf{21 \ m}}

 {\pink{\textsf{\textbf{Radius = 21 m}}}}

According to the question by using the formula of Area of a Circle, we get,

 \dashrightarrow \ {\green{\sf{Area \ of \ circular \ field = (\pi \times 21^2) \ m^2}}}

Solving the above equation,

 : \ \Longrightarrow \ {\sf{ \bigg ( \dfrac{22}{7} \times 21^2 \bigg ) \ m^2}}

 : \ \Longrightarrow \ {\sf{ \bigg ( \dfrac{22}{7} \times 21 \times 21 \bigg ) \ m^2}}

 : \ \Longrightarrow \ {\sf{ \bigg ( \dfrac{22}{7} \times 441 \bigg ) \ m^2}}

 : \ \Longrightarrow \ {\sf{ \bigg ( \dfrac{22}{{\cancel{7}}^{ \ 1}} \times {\cancel{441}}^{ \ 63} \bigg ) \ m^2}}

 : \ \Longrightarrow \ {\sf{(22 \times 63) \ m^2}}

 : \ \Longrightarrow \ {\sf{1,386 \ m^2}}

 {\blue{\textsf{\textbf{Area of the circular field = 1,386 sq. m.}}}}

Cost of cleaning the field = ₹ (1,386 × 2.35)

 : \ \Longrightarrow \ {\sf{\purple{Rs. \ 3257.1}}}

 {\boxed{\orange{\textsf{\textbf{Cost of cleaning the field is Rs. 3257.1}}}}}

Similar questions