Question

a hemispherical bowl made of brass has inner diameter 10.5 find the cost of tin plating it on the inside at the rate of 16rupees per 100 cm square​

Answer 1

Given :

• Diameter of a hemispherical bowl made of brass = 10.5 cm
• Cost of tin plating 100 cm² = Rs. 16

To find :

• Cost of tin plating the hemispherical bowl

Concept :

→ Formula to calculate radius :-

$\boxed{ \sf \pmb{Radius = \dfrac{Diameter}{2}}}$

→ Formula to calculate Curved surface area :-

$\boxed{ \sf \pmb{Curved~~surface~~area= 2\pi r^2}}$

where,

• Take π = 22/7
• r = radius

Solution :

Firstly, we will calculate the radius of the bowl :-

Radius :-

$\\ \dashrightarrow\sf \quad Radius = \dfrac{Diameter}{2}$

$\\ \dashrightarrow\sf \quad Radius = \dfrac{10.5}{2}$

$\\ \dashrightarrow\sf \quad Radius = \dfrac{ \not10.5}{ \not2}$

$\\ \dashrightarrow\sf \quad Radius = 5.25$

$\\ \sf \pmb{ \quad Radius \: of \: the \: bowl = 5.25 \: cm}$

Now, calculate the CSA of the bowl.

$\\ \dashrightarrow \sf \quad CSA = 2\pi r^2$

$\\ \dashrightarrow \sf \quad CSA = 2 \times \dfrac{22}{7} \times 5.25 \times 5.25$

$\\ \dashrightarrow \sf \quad CSA = 2 \times \dfrac{22}{ \not7} \times \not5.25 \times 5.25$

$\\ \dashrightarrow \sf \quad Circumference = 2 \times 22 \times 0.75 \times 5.25$

$\\ \dashrightarrow \sf \quad Circumference = 173.25$

$\\ \sf \pmb{\quad CSA \: of \: the \: bowl = 173.25 \: cm^2}$

Cost of tin plating 100 cm² of the bowl = Rs. 16

Cost of tin plating 1 cm² of the bowl = 16 ÷ 100 = Rs. 0.16

Cost of tin plating the hemispherical bowl = Cost of tin plating 1 cm² of the bowl × CSA of the bowl

$\\ \dashrightarrow \sf \quad Cost =0.16 \times 173.25$

$\\ \dashrightarrow \sf \quad Cost = 27.72$

$\\ \sf \pmb{ Cost \: of \: tin \: plating \: the \: bowl=Rs \: 27.72}$

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Know More :

• Area of circle = πr²
• Circumference = 2πr
• Diameter = 2 × Radius
• Surface area of sphere = 4πr²
• Volume of cylinder = πr²h
• Volume of cone = 1/3 πr²h
• Curved surface area of cone = πrl
• Total surface area of cone = πrl + πr²h
• Total surface area of cylinder = 2πrh + 2πr²