Answer

Verified

456.3k+ views

**Hint:**As we are asked for the cost of the canvas required for the tent it is sufficient to find the curved surface area of the cone because we just need the outer surface area in order to make the tent so we don’t include the area of the base. We can use the formula $\pi rl$ to calculate the curved surface area of the cone, but we need the slant height but it is not given in the problem so we can calculate the slant height using the formula $l = \sqrt {{h^2} + {r^2}} $. After finding the area we need to multiply it by 3.50, as it is the cost of canvas per ${m^2}$ to obtain the total cost of the canvas required for the tent.

**Complete step by step answer:**

Step 1:We are given the height and base diameter of the cone

Height, h =8m

Diameter, d =12m

From the diameter,let us calculate the radius ,r

$r = \dfrac{d}{2} = \dfrac{{12}}{2} = 6m$

Step 2:The formula of the curved surface area of a cone is $\pi rl$

So we need to find the slant height , l of the cone by using the formula below

$ \Rightarrow l = \sqrt {{h^2} + {r^2}} $

By substituting the values of h and r ,

$\begin{gathered}

\Rightarrow l = \sqrt {{{(8)}^2} + {{(6)}^2}} \\

\Rightarrow l = \sqrt {64 + 36} \\

\Rightarrow l = \sqrt {100} \\

\Rightarrow l = 10m \\

\end{gathered} $

Step 3: Now ,we have obtained our slant height .We can find the curved surface area of the cone

Curved Surface Area of the cone (CSA) =$\pi rl$sq ${m^2}$

$\begin{gathered}

\Rightarrow CSA = \dfrac{{22}}{7}*6*10 \\

\Rightarrow CSA = \dfrac{{22*60}}{\begin{gathered}

7 \\

\\

\end{gathered} } \\

\Rightarrow CSA = \dfrac{{1320}}{7} \\

\Rightarrow CSA = 188.57{\text{ }}{m^2} \\

\end{gathered} $

Step 4: We are given that the rate of canvas per ${m^2}$ is Rs.3.50.The canvas required for the conical tent is equal to the curved surface area.

Therefore ,the cost of canvas for $188.57{m^2} = 3.50*188.57 = 659.99$

By rounding off the value we get the cost to be Rs.660

**The correct option is d**

**Note:**Since its just the canvas required to make a tent, its enough if we find a curved surface area, not the total surface area. Many students make a mistake here.

Many students forget to find the slant height and directly substitute the value of height in the place of slant height.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which places in India experience sunrise first and class 9 social science CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE