- A cloth having an area of 165 m^2 is shaped into the form of a conical tent of radius 5 m . How many students can sit in the tent if a student, on an average, occupies 57m^2 on the ground?
- A cloth having an area of 165ð¦2 is shaped into a conical tent of radius 5ð¦.I How many students can sit in the tent if a student occupies 5/7ð¦2.ii Find the volume of air for each student.
- A cloth having an area of165 m2 is shaped into the form of a conical tent of radius 5 m , How many students can sit in the tent if a student, on an average, occupies5/7m2 on the ground?
Download: A cloth having an area of 165 m square
Size: 75.72 MB
A cloth having an area of 165 m^2 is shaped into the form of a conical tent of radius 5 m . How many students can sit in the tent if a student, on an average, occupies 57m^2 on the ground?
Ramaya decided to organise a small party with 11 persons on her birthday. There is small ground near to her home. She decided to arrange the party in this ground. She fixed the conical tent in the ground which can accommodate 11 persons. Each person must have 4 square metres of space on the ground and 2 0 m 3 of air to breath. Find the height of the conical tent.
A cloth having an area of 165ð¦2 is shaped into a conical tent of radius 5ð¦.I How many students can sit in the tent if a student occupies 5/7ð¦2.ii Find the volume of air for each student.
Step 1: Given information: The base radius of the conical tent ( r ) = 5 m The area occupied by a student = 5 / 7 m 2 Step 2: Calculate the number of students. First, we have to find the base area of the conical tent. The base area ( A ) is computed as: ⇒ A = π r 2 ⇒ A = 22 7 × 5 × 5 ⇒ A = 550 7 m 2 Since the area that is occupied by a student = 5 / 7 m 2, ∴The number of students that sit in the tent = 550 7 × 7 5 = 110 Step 3: Calculate the height of the conical tent. Since a cloth has an area of 165 m 2, which is shaped into a conical tent of the radius 5 m. ∴ The area of the conical tent = 165 ∴ π r l = 165 ⇒ 22 7 × 5 × l = 165 ⇒ l = 165 × 7 22 × 5 ⇒ l = 10 . 5 m Thus, the slant height ( l ) of the conical tent is 10 . 5 m. ∴ The height ( h ) of the conical tent is computed as: ⇒ h 2 = l 2 - r 2 ⇒ h 2 = ( 10 . 5 ) 2 - ( 5 ) 2 ⇒ h 2 = 110 . 25 - 25 ⇒ h 2 = 85 . 25 ⇒ h = 85 . 25 = 9 . 23 m Step 4: Calculate the volume of air for each student. ∴ V = 1 3 π r 2 h ⇒ V = 1 3 × 22 7 × ( 5 ) 2 × 9 . 23 ⇒ V = 241 . 74 m 3 Thus, the volume of air for each student = 241 . 74 110 = 2 . 198 m 3. Hence, (I) The number of students that sit in the tent is 110. (ii) The volume of air for each student is 2 . 198 m 3.
A cloth having an area of165 m2 is shaped into the form of a conical tent of radius 5 m , How many students can sit in the tent if a student, on an average, occupies5/7m2 on the ground?
According to the question, Area of cloth = 165 m 2 The radius of conical tent = 5 m Area covered by 1 student = 5 7 m 2 The curved surface area of cone = π r l Thus, the curved surface area of a conical; tent = π r l ⇒ 165 = 22 7 × 5 × l ⇒ l = 165 × 7 22 × 5 = 21 2 = 10 . 5 m Number of students = A r e a o f t h e b a s e A r e a o c c u p i e d b y o n e s t u d e n t Number of students = π r 2 5 7 = 22 7 × 5 2 5 7 = 22 × 5 = 110 Hence, number of students who can sit in the tent are 110.
