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3 years ago

36

Mathematics

1 answer:

alexdok [17]3 years ago

3 0

Step-by-step explanation:

w(idth) = 2.5 inches for both boxes

h(eight) = 10 inches for both boxes

l(ength)l(arge) = 8 inches

l(ength)s(mall) = 75% of ll (=> of 8 inches)

=> ls = 8 × 75/100 = 2 × 75/25 = 2 × 3 = 6 inches

vl (volume large) = 8 × 2.5 × 10 = 200 inches³

vs (volume small) = 6 × 2.5 × 10 = 150 inches³

the difference of these two volumes is 50 inches³

the units to be used is cubic inches (inches³). we are talking about volumes. not lengths (inches), not areas (inches²).

the reason - for a volume we need to multiply 3 lengths (measured in simple inches). so, inch multiplied by inch is inch². this multiplied by inch again is then inch³.

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The volume of the shape

We have a cylinder that is cut into two. Its external radius is 5ft, while its internal radius is 4ft.

External radius = internal radius + thickness

$\begin{gathered} \text{External radius = 4ft + 1ft } \\ =\text{ 5ft} \end{gathered}$

Internal radius = 4ft (given)

Recall that the volume(V) of a full cylinder is:

$V\text{ = }\pi r^2h$

Since the cylinder is cut into two, the volume(V) is:

$V\text{ = }\frac{\pi r^2h}{2}$

height (h) = 12ft (given)

The volume of the shape:

$\begin{gathered} =\text{ Volume of cylinder with a radius of 5ft - Volume of cylinder with a radius of 4ft} \\ =\text{ }\frac{\pi\text{ }\times5^2\text{ }\times\text{ 12}}{2}\text{ - }\frac{\pi\text{ }\times4^2\text{ }\times\text{ 12}}{2} \\ =\text{ 471.239 - }301.593 \\ =169.65ft^3 \end{gathered}$

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1 year ago

What is the volume, in cubic inches, of a cone that has a radius of 8 inches and a height of 12 inches? Use 3.14 for π , and rou

Doss [256]

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Step-by-step explanation:

First of all we have to find the base area

base area = radius^2 x 3.14 = 8^2 x 3.14 = 64 x 3.14 = 200,96 in^2

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V = (base area x height)/3

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2 years ago