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Chapter 8: Problem 9

find the volume of each cylinder. Round to nearest tenth. $$r=7 \mathrm{cm}, h=8 \mathrm{cm}$$

Short Answer

Expert verified
The volume is approximately 1231.5 cubic cm.

Step by step solution

01

Identify the formula

To find the volume of a cylinder, use the formula: \[ V = \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
02

Substitute the given values

Replace \( r \) with 7 cm and \( h \) with 8 cm in the formula: \[ V = \pi (7)^2 (8) \]
03

Calculate \( r^2 \)

Find the square of the radius: \[ 7^2 = 49 \]
04

Multiply by height

Multiply 49 (result from previous step) by the height 8: \[ 49 \times 8 = 392 \]
05

Multiply by \( \pi \)

Multiply the result by \( \pi \) (approximately 3.14159): \[ 392 \times \pi \approx 1231.5 \] Round the result to the nearest tenth: \[ 1231.5 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

geometry
Geometry is a branch of mathematics that deals with shapes, sizes, and properties of space. It involves understanding different figures and solids like circles, triangles, and cylinders. In our everyday life, geometry helps us see patterns, measure spaces, and design objects.

For this exercise, we focus on a cylinder, which is a 3D shape with two parallel circular bases and a curved surface that connects these bases.
cylinder volume formula
To find the volume of a cylinder, use this specific geometric formula: \( V = \pi r^2 h \). This formula calculates how much space the cylinder occupies. Here, \( V \) represents volume, \( r \) is the radius of its circular base, and \( h \) is its height.

Remember that \( \pi \) (pi) is approximately 3.14159. So, the volume calculation involves squaring the radius, multiplying it by the height, and then multiplying by \( \pi \).
mathematical calculations
Mathematical calculations require following specific steps precisely to achieve accurate results. Let鈥檚 see how this works in our cylinder volume example:
  • Step 1: Identify the formula: \( V = \pi r^2 h \)
  • Step 2: Substitute the given values where \( r = 7 \ \mathrm{cm} \ \) and \( h = 8 \ \mathrm{cm} \ \), resulting in \( V = \pi (7)^2 (8) \)
  • Step 3: Calculate \( r^2 \) (radius squared), which is 7*7 = 49
  • Step 4: Multiply 49 by the height (8), giving 392
  • Step 5: Finally, multiply 392 by \( \pi \) (approx 3.14159) to get the volume

Hence, the calculated volume is about 1231.5 cubic centimeters.
metric units
Metric units are a decimal-based system of measurement used by most countries worldwide. In this exercise, we measure dimensions in centimeters, a metric unit for length.

  • The radius ( r ) is 7 cm.
  • The height ( h ) is 8 cm.
  • We find the volume in cubic centimeters ( \( cm^3 \) ), reflecting the space inside the cylinder.

Metric units make mathematical calculations easier and more straightforward due to their base-10 nature. So, when measuring or calculating, always pay attention to the units you're using.

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Most popular questions from this chapter

find the volume of each cone. Round to the nearest tenth. $$r=6.9 \mathrm{cm}, h=14.2 \mathrm{cm}$$

determine whether the statement is true or false . If a cylinder and a cone have the same radius and height, the volume of the cylinder is three times the volume of the cone.

Find the surface area of each sphere. $$r=0.40 \mathrm{cm}$$

Find the surface area of each sphere. $$r=12 \mathrm{m}$$

Solve each applied exercise. A hanging pot is designed to hang from a tree and have flowers planted in it. The pot is a hemisphere and is made from plastic. The diameter of the pot is 14 inches. What is the surface area of the outside of the pot?
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