Once Five Friends Haviesh, Krishna, Akshay, Ankith and Devharsh 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. They made the Tent with a Height of 10 m and Diameter 14 m. The Remaining Cloth was used for the Floor.
(i) How much Cloth was used for the Floor?
a. 31.6 m²
b. 16 m²
c. 10 m²
d. 20 m²
(ii) What is the Volume of the Tent?
a. 300 m³
b. 160 m³
c. 153.3 m³
d. 500 m³
(iii) What was the Area of the Floor?
a. 50 m²
b. 100 m²
c. 150 m²
d. 154 m²
(iv) What was the Total Surface Area of the Tent?
a. 400 m²
b. 422.4 m²
c. 300 m²
d. 450 m²
Answers
✯ Question :
- Once Five Friends Haviesh, Krishna, Akshay, Ankith and Devharsh 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. They made the Tent with a Height of 10 m and Diameter 14 m. The Remaining Cloth was used for the Floor.
❃ Given : ✯ Total cloth ➠ 300 m²
ㅤㅤㅤ ✯ Height of tent ➠ 10 m
ㅤㅤㅤ ✯ Diameter of tent ➠ 14 m
❃ To Find : ✯ Cloth used for floor ➠ ?
ㅤㅤㅤ ✯ Volume of tent ➠ ?
ㅤㅤㅤ ✯ Area of floor ➠ ?
ㅤㅤㅤ ✯ T.S.A of the tent ➠ ?
❃ Formulae used :
- ✯ Radius ➠ Diameter/2
- ✯ slant height ➠ √(r² + h²)
- ✯ C.S.A. ➠ π × r × l
- ✯ Volume of a cone ➠ π r² (h/3)
- ✯ Base area of a cone ➠ π r²
- ✯ T.S.A. ➠ C.S.A. + Base Area of the conical tent .
✯ Explanation :
❖ Finding, cloth used for floor :
✫ Cloth used for floor ➠ Total cloth - Cloth used for tent (C.S.A.)
☆ C.S.A. (curved surface area) of the tent :
➯ radius (r) ➣ Diameter / 2
ㅤㅤㅤㅤㅤ ➣ 14 / 2
ㅤㅤㅤㅤㅤ ➠ 7 m.
➯ slant height (l) ➣ √(r² + h²)
ㅤㅤㅤㅤㅤ ㅤㅤ ➣ √(7² + 10²)
ㅤㅤㅤㅤㅤ ㅤㅤ ➣ √(49 + 10²)
ㅤㅤㅤㅤㅤ ㅤㅤ ➣ √(49 + 100)
ㅤㅤㅤㅤㅤ ㅤㅤ ➣ √149
ㅤㅤㅤㅤㅤ ㅤㅤ ➠ 12.2 m
➯ C.S.A. ➣ π × r × l
ㅤㅤㅤㅤ ➣ 22/7 × 7 × 12.2
ㅤㅤㅤㅤ ➣ 22 × 12.2
ㅤㅤㅤㅤ ➠ 268.4 m
➯ Cloth used for floor ➣ 300 m² - 268.4 m
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ 31.6 m²
.°. Hence, cloth used for floor is a) 31.6 m².
❖ Finding, volume of the conical tent :
➯ Volume ➣ π r² (h/3)
ㅤㅤㅤㅤㅤ ➣ (22/7) × 7² × (10/3)
ㅤㅤㅤㅤㅤ ➣ (22 × 7 × 10)/3
ㅤㅤㅤㅤㅤ ➣ 1540/3
ㅤㅤㅤㅤㅤ ➠ 513.3 m³
.°. Hence, volume of the tent is 513.3 m³.
❖ Finding, area of the floor :
➯ Area of the floor ➣ Base area of the conical tent
➯ Base area of a cone ➣ π r²
ㅤㅤㅤㅤㅤ ㅤㅤㅤㅤㅤ ➣ (22/7) × 7²
ㅤㅤㅤㅤㅤ ㅤㅤㅤㅤㅤ ➣ (22/7) × 49
ㅤㅤㅤㅤㅤ ㅤㅤㅤㅤㅤ ➣ 22 × 7
ㅤㅤㅤㅤㅤ ㅤㅤㅤㅤㅤ ➠ 154 m²
.°. Hence, area of the floor is d) 154 m².
❖ Finding, T.S.A. (Total surface area) of the tent :
➯ T.S.A. ➣ C.S.A. + Base Area of the conical tent
ㅤㅤㅤㅤ ➣ 268.4 + 154 m²
ㅤㅤㅤㅤ ➠ 422.4 m²
.°. Hence, T.S.A. of the tent is b) 422.4 m².