Question

The interior of a building is in the form of a right circular cylinder of radius 7m and height 6m, surmounted by a right circular cone of the same radius and of vertical angle of 60 degrees. Find the cost of painting the building from inside at the rate of Rs30 per meter square.

Answer 1

Here,
.............................
The R1 is the base of the cylinder
.…......….................
The R2 is the base of cone
...............................
The H1 is the height of the cylinder



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Answer 2

Given:

Cylinder of radius 7m and height 6 m

The circular cone surmounted have a vertical angle of 60°

The cost of painting is Rs 30/m²

To Find:

The cost of painting the inside

Solution

Find the slanted height of the cone:

radius = 7m

Let the height be H

$\sin \theta = \dfrac{\text{Opposite}}{\text{Hypotenuse}}$

$\sin(60 \div 2) = \dfrac{\text{7}}{\text{H}}$

$\sin(30) = \dfrac{\text{7}}{\text{H}}$

$H = \dfrac{7}{sin(30)}$

$H = 14 \text{ m}$

Find the surface area of the cone:

$\text{Surface area of a cone } = \pi rl$

$\text{Surface area of the cone } = \pi (7)(14)$

$\text{Surface area of the cone } = 308 \text{ m}^2$

Find the surface area of the cylinder:

$\text{Surface area of a cylinder } = 2\pi r h$

$\text{Surface area of the cylinder } = 2\pi(7)(6)$

$\text{Surface area of the cylinder } = 264 \text{ m}^2$

Find the total surface area:

$\text {Total surface area} = 308 + 264$

$\text {Total surface area} = 572 \text { m}^2$

Find the cost of painting:

$1 \text{ m}^2 = \text {Rs } 30$

$572 \text{ m}^2 =30 \times 572$

$572 \text{ m}^2 = \text {Rs } 17160$

Answer: The cost of painting is Rs 17160