Question

1) To make a conical tent $188\dfrac{4}{7}m²$ of tarpaulin is required.If the circumference of the base of tent be $35\dfrac{5}{7}m$ then find the height of the tent.

2) Volume of a rectangular parallelopiped is 2160cm^3 and the length of its diagonal is 25cm .If the length of the rectangular parallelopiped is 20cm then find its breadth and height.​

Answer 1

Answer 1) :-

given that,

• CSA of conical tent = 188(4/7) m² .
• Circumference of base of tent = 35(5/7) m .

we know that,

• CSA of cone = π * radius * slant height .
• Slant height = √[radius² + height²] .
• Circumference of base = 2 * π * radius .

so,

→ 2 * π * radius = 35(5/7)

→ 2 * (22/7) * r = (250/7)

→ 44 * r = 250

→ r = (250/44)

→ r = (125/22) m .

then,

→ CSA = 188(4/7)

→ (22/7) * (125/22) * L = (1320/7)

→ 125L = 1320

→ 25L = 264

→ L = (264/15) m .

therefore,

→ Height = √[L² - r²]

→ H = √[(264/25)² - (125/22)²]

→ H = √[(69696/625) - (15625/484)]

→ H = √(69696*484 - 15625*625) / (625*484)]

→ H = √(33732864 - 9765625) / (625 * 484)]

→ H = √[(23967239) / (625 * 484)]

→ H = (4895/25*22)

→ H ≈ 9 m. (Ans.)

_________________

Answer 2) :-

given that,

• Volume of rectangular parallelepiped = 2160 cm³.
• Diagonal = 25 cm.
• Length = 20 cm.

we know that,

• Volume of rectangular parallelepiped = Length * Breadth * Height .
• Diagonal = √(Length² + Breadth² Height²) .

Let us assume that, Breadth and height of the rectangular parallelepiped are Bcm and H cm.

so,

→ 20 * B * H = 2160

→ B•H = 108 cm².

also,

→ (25)² = 20² + B² + H²

→ 625 - 400 = B² + H²

→ B² + H² = 225 --------- Eqn.(1)

subtracting 2B•H from both sides of Eqn.(1),

→ B² + H² - 2B•H = 225 - 2*108

→ (B - H)² = 225 - 216

→ (B - H)² = 9

→ (B - H)² = (3)²

→ B - H = 3 cm. ---------- Eqn.(2)

also, adding 2B•H from both sides of Eqn.(1),

→ B² + H² + 2B•H = 225 + 2*108

→ (B + H)² = 225 + 216

→ (B + H)² = 441

→ (B + H)² = (21)²

→ B + H = 21 cm . ---------- Eqn.(3)

adding Eqn.(2) and Eqn.(3) now,

→ B - H + B + H = 3 + 21

→ 2B = 24

→ B = 12 cm. (Ans.)

putting value of B in Eqn.(2),

→ 12 - H = 3

→ H = 12 - 3

→ H = 9 cm. (Ans.)

Hence, Breadth and height of rectangular parallelepiped are 12 cm and 9 cm respectively .

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Answer 2

solution of questions no.1....

solution of questions no.1....height of the tent= 9cm