a conical tent is of 10m high and the radius of its base is 24m find
slant height of the tent cost of the canvas requered to make the tank if the cost 1 m canvas is of rupeess 70
Answers
Given :
• Height of a concial tent = 10 m
• Radius of its base = 24 m
To find :
• Slant height of the tent
• Cost of the canvas required to make the tank if the cost 1 m canvas is of Rs. 70
Analysis :
Here, we have to find the slant height so, for that we will directly use the formula of slant height.
To find the cost of canvas required to make the tank we will firstly calculate the curved surface area of the cannvas and then mulitply it by rate. The resultant value will be the required answer.
Formula to find the slant height of cone = √(r² + h²)
Formula to find the curved surface area of cone = πrl
where,
- Take π = 22/7
- r = radius
- h = height
- l = slant height of cone
Solution :
Calculating the slant height of tent :-
→ Slant height = √(r² + h²)
→ Substituting the given values :-
→ Slant height = √(24² + 10²)
→ Slant height = √576 + 100)
→ Slant height = √676
→ Slant height = √(26 × 26)
→ Slant height = ± 26 Reject -ve
→ Slant height = 26
Therefore, the slant height of the tent = 26 m
Now, calculating the curved surface area of the tent :-
→ Curved surface = πrl
→ Substituting the given values :-
→ Curved surface = 22/7 × 24 × 26
→ Curved surface area = 1961.14
Therefore, the curved surface area of tent = 1961.14 m²
Total cost required to make the tent = Curved surface area × Rate
→ Total cost = 1961.14 × 70
→ Total cost = 137,279.80
Therefore, the total cost = Rs. 137,279.80