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nlexa [21]
3 years ago
13

4. A glass decoration is made from a cylinder and cone that have the same height and share a base. The cone fits exactly inside

the cylinder. Blue sand fully fills the cone, and green sand fully fills the space between the cone and the cylinder. The radius of base is 5 cms, and the height is 24cms. In terms of pi, what is the volume of green sand between the cone and the Cylinder.

Mathematics
1 answer:
Viktor [21]3 years ago
4 0

Answer:

<u>Volume of Green Sand =  </u>400 \pi<u>  cubic centimeters</u>

Step-by-step explanation:

<em><u>The image is shown below.</u></em>

<em><u /></em>

We need to find volume of cone and volume of cylinder.

The green sand space is:

Volume of Cylinder - Volume of Cone

Formulas:

Volume of Cylinder = \pi r^2 h

Volume of Cone = \frac{1}{3}\pi r^2 h

Given, r = 5 and h = 24 (in centimeters), we find the green sand volume:

Volume of Green Sand = Volume of Cylinder - Volume of Cone = \pi r^2 h - \frac{1}{3} \pi r^2 h = \frac{2}{3} \pi r^2 h = \frac{2}{3} \pi (5)^2 (24) = \frac{2}{3} \pi (25)(24) = 400 \pi

<u>Volume of Green Sand =  </u>400 \pi<u>  cubic centimeters</u>

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HELP!! Suppose the area of a circle is 201.0624 square feet. What's the diameter of the circle? (Use π = 3.1416.)
Liono4ka [1.6K]

<u>Answer</u>

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<u>Explanation</u>

The area of a circle is given by the formula:

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r² = 201.0624/3.1416

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3 years ago
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Answer:

7.7 km

Explanation:

Use cosine rule as here given two sides and one angle.

Cosine rule states:

a² = b² + c² - 2bc cos(A)

While solving, treat a = 7.5 km as to that opposite angle is given of 68°

then b = missing side, c = 5.2 km, A = 68°

Applying rule:

7.5² = b² + 5.2² - 2(b)(5.2) cos(68)

56.25 = b² + 27.04 - 3.8959b

56.25 - 27.04 = b² - 3.8959b

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apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]

\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0

\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}

\sf b = 7.69 291 \quad or \quad b = -3.797

\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)

As length cannot be negative. Hence the value of b is only 7.7 km

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2 years ago
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