Question

The slant height and height of a cone shaped structure are 101 m and 99 m. Find the cost of painting the structure at Rs. 80 per square meter.

Answer 1

GIVEN:

• Slant height (l) = 101 m
• Height (h) of the cone = 99 m

TO FIND:

• What is the cost of painting the structure at Rs. 80 per square meter.

SOLUTION:

Let the radius of the cone be 'r' m

To find the radius of the cone, we use the formula

$\large{\boxed{\bf{\star \: l^2 = h^2 + r^2 \: \star}}}$

On putting the given values in the formula, we get

$\rm{\hookrightarrow (101)^2 = (99)^2 + (r)^2 }$

$\rm{\hookrightarrow 10201 = 9801 + r^2}$

$\rm{\hookrightarrow 10201 - 9801 = r^2}$

$\rm{\hookrightarrow 400 = r^2}$

$\rm{\hookrightarrow \sqrt{400} = r }$

$\large\underline\mathbf{\hookrightarrow \star \: 20 \: m = r \: \star}$

We know that the formula for finding the CSA of the cone is:-

$\large{\underline{\boxed{\bf{\star \: CSA = \pi r l \: \star}}}}$

According to question:-

Take π = 3.14

$\rm{\hookrightarrow CSA = 3.14 \times 20 \times 101 }$

$\large\underline\mathbf{\hookrightarrow \star \: CSA = 6342.8 \: m^2 \: \star }$

• 1 m² = Rs. 80
• 6342.8 m² = 6342.8 $\times$ 80
• 6342.8 m² = Rs. 507424

❝ Hence the cost of painting the structure of 6342.8 m² is Rs. 507424 ❞

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