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Rudiy27
3 years ago
7

A cylinder has a height of 18 millimeters and a radius of 18 millimeters. What is its volume? Use ​ ≈ 3.14 and round your answer

to the nearest hundredth.
Mathematics
1 answer:
Sholpan [36]3 years ago
4 0

Answer:

18312.5mm³

Step-by-step explanation:

Given parameters:

Height of cylinder  = 18mm

radius  = 18mm

Unknown:

Volume of the cylinder = ?

Solution:

The volume of cylinder is given as;

  Volume  = π r ² h

Insert the given parameters and solve;

  Volume  = 3.14 x 18² x 18

  Volume  = 18312.5mm³

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Find the area of the shaded region. Round to the nearest hundredth where necessary (2 decimal places
suter [353]

Answer:

117 in²

<u>Finding the area of the trapezoid:</u>

First, we need to find the area of the trapezoid formed by the dotted lines. The formula for finding the area of the trapezoid is "(a₁ + a₂)h/2".

[Where, a₁ = shorter parallel side; a₂ = longer parallel side]

⇒ (a₁ + a₂)h/2 = Area of trapezoid

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⇒ Area of trapezoid = (40)15/2 = (20)15 = 300 in²

<u>Reviewing on how to find the area of the unshaded region:</u>

To find the area of the shaded region, we need to subtract the area of the unshaded region from the area of the trapezoid. In this case, the unshaded region is a triangle whose base is 26 inches. To find the area of the triangle, we need to use the formula 1/2 x Base x Height. We are given the base, but the height is unknown.

<u>Determining the height:</u>

We are given a small side length "6 inches" and the height of the trapezoid "15 inches". If we subtract the small side length from the height of the trapezoid, we will obtain the height of the triangle.

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Now, let's substitute the base and the height in the formula to find the area of the triangle

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⇒ 1/2 x 26 x 9

⇒ 13 x 9

⇒ 117 in²

<u>Determining the area of the shaded region:</u>

Finally, let's subtract the area of the unshaded region from the area of the trapezoid to obtain the area of the shaded region.

⇒ Area of trapezoid - Area of unshaded region = Area of shaded region

⇒ 300 - 117 = Area of shaded region

⇒ 183 in² = Area of shaded region

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