Question

A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent. If the cost of 1 m² canvas is Rs. 70, find the cost of the canvas required to make the tent.

Answer 1

The slant height of the tent is 26 m. The cost of the canvas required to make the tent 137280 Rupees.

Step-by-step explanation:

• Given data

        Height of cone (H) = 10 m

        Radius of cone (R) = 24 m

        Cost of canvas per square meter =70 Rupees

        Slant height of cone = L = Unknown

• We know relation between slant height, height and radius of cone is given below

        $\mathbf{L=\sqrt{R^{2}+H^{2}}}$

        On putting respective value in above equation

        $\mathbf{L=\sqrt{24^{2}+10^{2}}}$

        $\mathbf{L=\sqrt{576+100}}$

        $\mathbf{L=\sqrt{676}=26 \ m}$   This is slant height of cone

• From formula of curved surface area of cone

        $\mathbf{\textrm{Curved surface area of cone}=\pi \times R\times L}$

        On putting respective value in above equation

        $\mathbf{\textrm{Curved surface area of cone}=\frac{22}{7} \times 24\times 26}$

• Now total cost = Area ×Price rate

       Total cost of canvas $\mathbf{=\frac{22}{7} \times 24\times 26\times 70=137280 \ Rupees}$

Answer 2

Given:-

• A conical tent is 10 m high and the radius of its base is 24 m.
• The cost of 1 m² canvas is Rs. 70,

To find:-

• Find the slant height of the tent.
• Find the cost of the canvas required to make the tent.

Solutions:-

• length = 10m
• base radius = 24m

Slant height, l = √r² + h²

= √24² + 10²

= √576 + 100

= √676

= 26m

Hence, the slant height of the cone is 26m

curved surface area = πrl

Now,

Substituting the value of r = 24m and slant height = 26m

and using π = 22/7 in the formula of CSA.

curved surface area = πrl

= 22/7 × 24 × 26

= 13728/7

The cost of the canvas is Rs 70 per m².

The total cost of canvas = (total curved surface area) (cost per m²)

= 13728/7 × 70

= 13728 × 10

= 137280

Hence, the total amount required to construct the tent is Rs. 137280.