Question

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying 300 m² cloth with them. As shown in the figure they made the tent with height 10 m and diameter 14 m. The remaining cloth was use for the floor. 1. How much Cloth was used for the floor? 2 What was the volume of the tent? What was the volume of the tent? 4. What was the total surface area of the tent? *​

Answer 1

Answer:

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season they did not get a proper Hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying 200 sq.m cloth with them.

Answer 2

Answer:

(1) amount of cloth used for the floor = 31.85 m²

(2) volume of tent = 512.86 m³

(4) total surface area of tent = 422.016 m²

Step-by-step explanation:

given, height of the tent = 10 m and diameter = 14 m

radius = 7 m

and, they carried 300 m² cloth with them

slant height of the cone = √(10²+7²) = √149 = 12.2m²

curved surface area of cone, (CSA) = πrl

area of cloth used for the curved surface of tent = 3.14 × 7 × 12.2

       = 268.15 m²

(1) amount of cloth used for the floor = total cloth they carried - area of cloth used for the cutved curface of the tent

        = 300 - 268.15 = 31.85 m²

(2) volume of cone = $\frac{1}{3}$πr²h

volume of tent = $\frac{1}{3}$ × 3.14 × 7² × 10 = 512.86 m³

(4) total surface area(TSA) of cone = πr(l+r)

total surface area of tent = 3.14 × 7× (12.2+7) = 3.14×7×19.2

          = 422.016 m²