Question

A solid is composed of a cylinder with hemisphe
is composed of a cylinder with hemispherical ends. If the whole
hemispherical ends
length of the solid is 105 cm and the radius of each of the hemispherican
IS 17.5 cm, find the cost of polishing its surface at the rate of 5rupees per cm^2​

Answer 1

Answer:

Rs. 57750

$\rule{200}2$

Step-by-step explanation:

Given:-

• A solid is composed of a cylinder with hemisphere on it's ends.
• Length of sold is 105 cm
• Radius of hemisphere = radius of cylinder = 17.5 cm.

Find:-

The cost of polishing the surface of solid at the rate of Rs. 5 per cm².

Solution:-

Total surface area of solid = Curved surface area of two cylinder + Curved surface area of two hemispheres

=> 2πrh + 2(2πr²)

=> 2πr(h + 2r)

=> 2 × 22/7 × 17.5 [h + 2(17.5)]

=> 110 (h + 35) ...(1)

Now,

Height of cylinder + height of hemisphere = Total height of a solid

=> h + 2r = 105

=> h = 105 - 2r

=> h = 105 - 2(17.5)

=> h = 105 - 35

=> h = 70 cm

Substitute value of h in equation (1)

=> 110 (70 + 35)

=> 110 (105)

=> 11550 cm²

•°• Cost of polishing the surface of solid at the rate of Rs. 5 per cm² = 11550 × 5

=> Rs. 57750

Answer 2

Given :---

• solid is composed of a cylinder + 2 hemisphere on both ends .
• Total Length of solid = 105cm
• Radius of Each Hemisphere = 17.5cm.
• cost of Polishing @ Rs.5/cm²

Formula used :----

• CSA of cylinder = 2πrh
• CSA of Hemisphere = 2πr²
• Total Area to be painted = CSA of cylinder + CSA of 2 Hemisphere .

$\pink{\bold{\underline{\underline{<strong>solution</strong><strong>(</strong><strong>1</strong><strong>)</strong>}}}}$

First we need to Find Height of cylinder ...

[ Refer to image First ] .

As in the diagram we can easily see that, Total height of solid is equal to = Height of cylinder + radius of upper hemisphere + radius of lower hemispher .

And radius of both hemisphere is same = 17.5cm .

Hence , Height of cylinder = 105 - (2×17.5) = 70cm.

Now, Let Find out CSA of Cylinder First ,

since radius of hemisphere = radius of cylinder = 17.5cm

Putting values we get,,

$CSA \: of \: Cylinder = 2 \times \frac{22}{7} \times 17.5 \times 70 \\ \\ \implies \: CSA = 7700 \: {cm}^{2}$

Now,

CSA of both hemisphere = 2(2πr²) = 4πr² ,

Putting values we get,

$CSA \: of \: both \: hemisphere = 4 \times \frac{22}{ \cancel7} \times \cancel{17.5} \times 17.5 \\ \\ \implies \: CSA = 3850 \: {cm}^{2}$

Total CSA to be Painted = 7700+3850 = 11550 cm²

Now,

it is given that , cost or of polishing is = 5 per cm²

so, overall cost of painting solid = 11550 × 5 = Rs.57750

___________________________________

$\red{\bold{\underline{\underline{Solution(2)}}}}$

we can solve it easily by taking common , and since we know that, (2r + h) = Total height of solid = 105 cm.

so,

2πrh + 2(2πr²)

Taking 2πr common we get,

→ 2πr(h+2r)

putting value of (2r+h) = 105cm.

[ we dont need to Find height or of cylinder or anything]

→ 2πr × 105

putting r = 17.5cm we get,

$\implies \: 2 \times \frac{22}{ \cancel7} \times 17.5 \times \cancel{105} = 11550 \: cm^{2}$

$\textbf{</strong><strong>we</strong><strong> </strong><strong>get</strong><strong> </strong><strong>same</strong><strong> </strong><strong>value</strong><strong> </strong><strong>this</strong><strong> </strong><strong>time</strong><strong> </strong><strong>also</strong><strong>.</strong><strong>}$

so, Rate of painting will be = 11550 × 5 = Rs.57750

$\textbf{</strong><strong>Hope</strong><strong> </strong><strong>it</strong><strong> </strong><strong>Helps</strong><strong> </strong><strong>you</strong><strong>}$