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Dovator [93]
3 years ago
6

A conical cup is made from a circular piece of paper with radius 4 cm by cutting out a sector and joining the edges as shown bel

ow. Suppose θ = 3π/2.Find the volume V of the cup.

Mathematics
1 answer:
a_sh-v [17]3 years ago
4 0

Answer:

  V = 3π√7 cm³ ≈ 24.94 cm³

Step-by-step explanation:

The radius of the finished cone can be found from the circumference of the finished cone, which is 3/4 of the circumference of the original paper circle.

  Ccone = (3/4)Ccircle = (3/4)(2π(4 cm)) = 6π cm

This is related to the cone radius (x) by ...

  Ccone = 2πx = 6π cm

  x = 3 cm . . . . . . . . . 3/4 of the circle's radius

The height of the cone is given by the Pythagorean theorem:

  (4 cm)² = h² + x²

  h² = (4 cm)² -(3 cm)² = (16 -9) cm²

  h = √7 cm

Now, we can use the formula for the volume of a cone:

  V = (1/3)πr²h

  = (1/3)π(3 cm)²(√7 cm)

  V = 3π√7 cm³ ≈ 24.94 cm³

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

A = Pe^{rt}, where

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∵ Angus has $3,000 he want to invest

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∴ t = 8

→ Substitute them in the rule above to find r

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→ Divide both sides by 3000

∴ \frac{11}{6} = e^{8r}

→ Insert ㏑ in both sides

∵ ㏑( \frac{11}{6} ) = ㏑(e^{8r})

→ Remember ㏑(e^{n}) = n

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→ Divide both sides by 8

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∴ r = 7.576697545 %

→ Round it to the nearest hundredth

∴ r ≅ 7.58

∴ The interest rate is 7.58%

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Maurinko [17]

Answer:

a

Step-by-step explanation:

3 0
2 years ago
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