A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹4989.60. If the cost of white-washing is ₹20 per square meter, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome​

Answers 2

Answer:

Hope it will help you

plz plz plz I'm in need plz

Step-by-step explanation:

Total cost = 498.96 Rs. => Area whitewashed = 249.48 Rs. And according to the question, the area whitewashed is Curved surface area of hemisphere. => 523.908 m³ (approx.)

[tex] \star \; {\underline{\boxed{\pmb{\red{\frak{ \; Given \; :- }}}}}} [/tex]

  • Cost of white - washing = Rs.4989.60
  • Rate of white - washing = Rs.20

[tex] \\ \\ [/tex]

[tex] \star \; {\underline{\boxed{\pmb{\blue{\frak{ \; To \; Find \; :- }}}}}} [/tex]

  • Inside surface area of the dome = ?
  • Volume of the air inside the dome = ?

[tex] \\ \\ [/tex]

[tex] \star \; {\underline{\boxed{\pmb{\orange{\frak{ \; SolutioN \; :- }}}}}} [/tex]

[tex] \maltese [/tex] Formula Used :

  • [tex] {\underline{\boxed{\pmb{\sf{ CSA{\small_{(Hemisphere)}} = 2 \pi {r}^{2} }}}}} [/tex]

  • [tex] {\underline{\boxed{\pmb{\sf{ Volume{\small_{(Hemisphere)}} = \dfrac{2}{3} \pi {r}^{3} }}}}} [/tex]

[tex] \\ \qquad{\rule{150pt}{2pt}} [/tex]

[tex] \maltese [/tex] How to Calculate :

[tex] \longrightarrow [/tex] Here, we can Calculate the Surface Area by dividing the Cost with the Rate . And for calculating the Air sinsid the dome we need to calculate the Volume . As we know for calculating it we should get the Radius first .So, Let's Solve :

[tex] \\ \qquad{\rule{150pt}{2pt}} [/tex]

[tex] \maltese [/tex] Calculating the Surface Area :

[tex] {\longmapsto{\qquad{\sf{ Surface \; Area = \dfrac{ Cost }{Rate} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \; Area = \dfrac{ 4989.60 }{20} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \; Area = \dfrac{ 498960 }{20 \times 100} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \; Area = \cancel\dfrac{ 498960 }{2000} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\pink{\sf{ Surface \; Area = 249.48 \; {m}^{2} }}}}}}}} [/tex]

[tex] \\ \qquad{\rule{150pt}{2pt}} [/tex]

[tex] \maltese [/tex] Calculating the Radius :

[tex] {\dashrightarrow{\qquad{\sf{ CSA = 2 \pi {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 249.48 = 2 \times \dfrac{22}{7} \times {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 249.48 \times 7 = 2 \times 22 \times {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 1746.36 = 44 \times {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{1746.36}{44} = {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{1746.36}{44} = {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 39.69 = {r}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \sqrt{39.69} = r }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\purple{\sf{ Radius = 6.3 \; cm }}}}}}}} [/tex]

[tex] \\ [/tex]

[tex] \\ \qquad{\rule{150pt}{2pt}} [/tex]

[tex] \maltese [/tex] Calculating the Volume of air :

[tex] {\implies{\qquad{\sf{ Volume = \dfrac{2}{3} \pi {r}^{3} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \dfrac{2}{3} \times \dfrac{22}{7} \times {6.3}^{3} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \dfrac{2}{3} \times \dfrac{22}{7} \times \bigg( {\dfrac{63}{10}} \bigg)^{3} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \dfrac{2}{3} \times \dfrac{22}{\cancel7} \times \dfrac{\cancel{63}}{10} \times \dfrac{63}{10} \times \dfrac{63}{10} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \dfrac{2}{3} \times 22 \times \dfrac{9}{10} \times \dfrac{63}{10} \times \dfrac{63}{10} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \dfrac{1571724}{3000} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = \cancel\dfrac{1571724}{3000} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\red{\sf{ Volume = 523.9 \; {m}^{3} \; \bigg\lgroup Approx. \bigg\rgroup }}}}}}}} [/tex]

[tex] \\ \qquad{\rule{150pt}{2pt}} [/tex]

[tex] \maltese [/tex] Therefore :

❛❛ Surface Area of the Dome is 249.48 cm² and the Volume of air inside the dome is 523.9 cm³ . ❜❜

[tex] \\ {\underline{\rule{300pt}{9pt}}} [/tex]

If you know the answer add it here!

Can't find the answer?

Log in with Google

or

Forgot your password?

I don't have an account, and I want to Register

Choose a language and a region
How much to ban the user?
1 hour 1 day 100 years