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3 years ago

What is the volume of a hemisphere with a radius of 9.2 cm, rounded to the nearest tenth of a cubic centimeter?

Mathematics

1 answer:

NARA [144]3 years ago

6 0

Answer:

volume of the hemisphere ≈1577.5 cm³

Step-by-step explanation:

To find the formula for calculating the volume of a hemisphere, we will follow the steps below:

write the formula for calculating the volume of a hemisphere.

volume of a hemisphere = volume of a sphere ÷2

= $\frac{4}{3}$ πr³ ÷ 2

= $\frac{2}{3}$ πr³

WHERE r is the radius

from the question given, radius= 9.2 cm

π is a constant and is ≈ 3.14

we can now proceed to insert the values into the equation

volume of a hemisphere = $\frac{2}{3}$ πr³

= $\frac{2}{3}$ × 3.14 ×9.2³

= $\frac{2}{3}$ × 3.14 ×753.571

≈1577.5 cm³ to the nearest tenth of cubic centimeter

volume of the hemisphere ≈1577.5 cm³

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Step-by-step explanation:

Given

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We have:

$f(x) = e^{-4x};\ [0,2]$

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To do this, we use:

$f'(c) = \frac{f(b) - f(a)}{b - a}$

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$f'(c) = \frac{f(2) - f(0)}{2 - 0}$

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$f'(c) = \frac{-0.99966453738}{2}$

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This implies that:

$f'(c) = -4e^{-4c}$

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$f'(c) = -0.4998$

$-4e^{-4c} =-0.4998$

Divide both sides by -4

$e^{-4c} =\frac{-0.4998}{-4}$

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$-4c =-2.0798$

Solve for c

$c =\frac{-2.0798}{-4}$

$c =0.51995$

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