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2 years ago

8

Find the volume of a right circular cone that has a height of 12.2 cm and a base with a circumference of 18.5 cm. Round your ans

wer to the nearest tenth of a cubic centimeter.

1 answer:

loris [4]2 years ago

5 0

Answer:

110.7 cm³ to the nearest tenth

Step-by-step explanation:

The volume V of a cone whose circular base has a radius r and a height h is given as

V = 1/3 πr²h

where π = 22/7

Given the circumference of the circular base as 18.5cm, we must find the radius before we can computed the volume. The relationship between the radius and the circumference is such that the circumference C

= 2πr

hence,

r = C/2π

= 18.5/2π

since the height of the cone is 12.2 cm, the volume V

= 1/3 * π * (18.5/2π)² * 12.2

= 110.71 cm³

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(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

$Area = 64.8$

Required

Calculate the perimeter.

Area is calculated as:

$Area = L * W$

Where

$L = Length$ and $W = Width$

Substitute 64.8 for Area

$64.8 = L * W$

Make L the subject:

$L = \frac{64.8}{W}$

Perimeter is calculated as:

$P = 2 * (L + W)$

Substitute 64.8/W for L

$P = 2 * (\frac{64.8}{W} + W)$

$P = \frac{129.6}{W} + 2W$

To solve further, we take the derivative of P and set it to 0, afterwards.

$dP = -\frac{129.6}{W^2} + 2$

Set to 0

$0 = -\frac{129.6}{W^2} + 2$

Collect Like Terms

$\frac{129.6}{W^2} = 2$

Cross Multiply:

$2W^2= 129.6$

Divide through by 2

$W^2 = 64.8$

Take square roots

$W = \sqrt{64.8$

$W = 8.05$

Recall that:

$L = \frac{64.8}{W}$

So:

$L= \frac{64.8}{8.05}\\$

$L= 8.05$

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Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

Required

Solve

$Tenths = \frac{1}{10}$

So, the expression becomes:

((1 Group of $10 * \frac{1}{10}$ ) and (1 group of $8 * \frac{1}{10}$ ))/(6 groups of $3 * \frac{1}{10}$ )

This gives:

((1 Group of $\frac{10}{10}$ ) and (1 group of $\frac{8}{10}$ ))/(6 groups of $\frac{3}{10}$ )

Group means product, so the expression becomes:

$\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}$

And, as used here means addition

$\frac{(1 * \frac{10}{10} + 1 * \frac{8}{10})}{6 * \frac{3}{10}}$

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$\frac{(1 + 0.80)}{1.80}$

$\frac{1.80}{1.80}$

$= 1.00$

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