Question

The outer and inner diameters of a hemispherical bowl are 17cm and 15cm. Find the cost of polishing it all over at Rs 2.50 per cm2

Answer 1

Given:

Outer diameter (D) = 17cm

Inner diameter (d) = 15cm

Cost of polishing it per cm² = ₹2.50

To find:

Total surface of the hemispherical bowl.

The cost of polishing it all over at Rs 2.50 per cm²

Solution:

First we will find the C.S.A. of inner bowl

So, this implies 2πr²

2×22/7×(15)²

44/7×225

1414.3 cm²

Also the C.S.A of outer bowl = 2πR²

So, this implies 2×22/7×(17)²

44/7×289

1816.6 cm²

Now, the area of its ring = 2π(R-r)²

So, this implies 2×22/7×(17-15)²

44/7×(2)²

44/7×4

176/7

25.1 cm²

Now, Total surface area of the hemispherical bowl = C.S.A. of the outer bowl + C.S.A. of the inner bowl + Area of its ring

So, this implies 1414.3 + 1816.6 + 25.1 = 3256 cm²

So, The cost of polishing 3256 cm²= ₹2.50×3256

= ₹8,140

Hence the cost of polishing it all over = ₹8140

Hope it helps you.

Please mark me as the brainliest.

Answer 2

$\underline{\underline{ \huge{\bf{ \red{ \bigstar \: given}}}}}$

$\tt{ \bullet \: given \: a \: hemispherical \: bowl}$

$\mathtt{\bullet \:inner \: diameter \: of \:bowl = 15 \: cm } \\ \tt{inner \: radius \: of \: bowl \: ,r= \frac{15}{2} \: cm }$

$\tt{ \bullet \: outer \: diameter \: of \: bowl = 17 \: cm} \\ \tt{outer \: radius \: of \: bowl \: ,R= \frac{17}{2} \: cm }$

$\tt{ \bullet \: rate \: of \: polishing =2.50 \: per \: {cm}^{2} }$

$\underline{ \underline{ \huge{ \bf{ \red{ \bigstar \: to \: find}}}}}$

$\tt{ \bullet \: cost \: of \: polishing \: it \: all \: over}$

$\underline{ \underline{ \huge{ \bf{ \red{ \bigstar \: formula \: used}}}}}$

$\star\tt{curved\: surface \: area \: of \: hemisphere}$

$\tt{is \: given \: by}$

$\boxed{ \tt{2\pi {(radius)}^{2} }}$

$\star \tt{area \: of \: circle \: is \: given \: by}$

$\boxed{ \tt{\pi {(radius) }^{2} }}$

$\underline{ \underline{ \huge{ \bf{ \red{ \bigstar \: solution}}}}}$

$\tt{tsa \: of \: given \: hemispherical \: bowl}$

$\tt{ =2\pi {R}^{2} + 2\pi {r}^{2} + (\pi {R}^{2} - \pi {r}^{2} ) }$

$\tt{ =3\pi {R}^{2} + \pi {r}^{2} }$

$\tt{ = (3 \times \frac{22}{7} \times \frac{17}{2}\times\frac{17}{2}) +( \frac{22}{7} \times \frac{15}{2}\times\frac{15}{2} ) }$

$\tt{ = \frac{22}{7}( \frac{867}{4} + \frac{225}{4} ) = \frac{22}{7} \times 273}$

$\tt{ = 858 \: {cm}^{2} }$

________________________

$\tt{cost \: of \: polishing}$

$\tt{ = 858 \times 2.50 \: Rs}$

$\blue{\tt{ = 2145 \: Rs \: }}$

________________________