Question

The outer and inner diameters of a hemispherical bowl are 17cm and 15 cm. Find cost of polishing it all over at 50 paise per cm square

Answer 1

Given :

• The outer and inner diameters of a hemispherical bowl are 17cm and 15 cm.

To find :

• Cost of polishing it all over at 50 paise per cm square =?

Formula Used :

• Curved surface area of hemisphere = 2πr².

Step-by-step explanation :

It is Given that,

The outer diameter of hemispherical bowl = 17 cm.

As We know that,

Radius = Diameter/2

So, Outer radius of hemispherical bowl = 17/2 = 8.5 cm.

And,

The inner diameter of hemispherical bowl = 15 cm.

Similarly,

Radius = 15/2 = 7.5 cm

Now,

As We know that,

Curved surface area of hemisphere = 2πr².

Substituting the values in the above formula, we get,

= 2 × π × (8.5)²

= 2 × 22/7 × 8.5 × 8.5

= 44/7 × 72.25

= 44 × 10.32

= 454.08.

Therefore, Curved surface area of outer hemispherical bowl = 454.08 cm².

Similarly,

= 2 × π × (7.5)²

= 2 × 22/7 × 56.25

= 2 × 22 × 8.03

= 353.32

Therefore, Curved surface area of inner hemispherical bowl = 353.32 cm².

Now,

Total Surface area of hemispherical bowl,

= 454.08 + 353.32

= 807.4

Therefore, Total Surface area of hemispherical bowl = 807.4 cm².

Now,

Cost of polishing it all over at 50 paise per cm square,

= 807.4 × 50

= 40,370

Therefore, Cost of polishing it all over at 50 paise per cm² = 40,370 paise.

Answer 2

✯✯ QUESTION ✯✯

The outer and inner diameters of a hemispherical bowl are 17cm and 15 cm. Find cost of polishing it all over at 50 paise per cm square ..

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

➥For Outer Hemisphere : -

$\longmapsto\tt{Diameter(d)=17cm}$

➮As we know that Radius is half of Diameter ... So ,

$\longmapsto\tt{Radius(r)=\cancel\dfrac{17}{2}}$

$\longmapsto\tt{R=8.5cm}$

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\red{\sf{C.S.A\:of\:hemisphere=2\pi{{r}^{2}}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{2\times\dfrac{22}{7}\times{8.5}\times{8.5}}$

$\longmapsto\tt{\cancel\dfrac{317900}{700}}$

$\longmapsto\tt\boxed{454.08 {cm}^{2}}$

☛So , Curved Surface Area of Outer Hemispherical bowl is 454.08 cm²..

_______________________

➥For Inner Hemisphere : -

$\longmapsto\tt{Diameter(d)=15cm}$

➮As we know that Radius is half of Diameter ... So ,

$\longmapsto\tt{Radius(r)=\cancel\dfrac{15}{2}}$

$\longmapsto\tt{R=7.5cm}$

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\pink{\sf{C.S.A\:of\:hemisphere=2\pi{{r}^{2}}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{2\times\dfrac{22}{7}\times{7.5}\times{7.5}}$

$\longmapsto\tt{\cancel\dfrac{247500}{700}}$

$\longmapsto\tt\boxed{353.32 {cm}^{2}}$

☛So,Curved Surface of Inner Hemispherical Bowl is 353.32cm²

➥Now ,

$\longmapsto\tt{Total\:Surface\:Area=Inner\:Area+Outer\:Area}$

$\longmapsto\tt{353.32+454.08}$

$\longmapsto\tt\boxed{807.4cm}$

➮Cost of polishing it at 50p per cm² : -

$\longmapsto\tt{807.4\times{50}}$

$\longmapsto\tt\boxed{40,370}$

☛So , Cost of polishing it at 50p per cm² is 40,370..