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Chapter 9: Problem 292

Solve. Round answers to the nearest hundredth. Snack pack A snack pack of cookies is shaped like a cylinder with radius 4 cm and height 3 cm. Find its (a) volume and (b) surface area.

Short Answer

Expert verified
Volume: 150.80 cm鲁, Surface Area: 175.93 cm虏

Step by step solution

01

Understand the formulas

For the volume of a cylinder, the formula is \[ V = \pi r^2 h \]. For the surface area, the formula is \[ SA = 2 \pi r (r + h) \].
02

Identify given values

The radius (r) is 4 cm and the height (h) is 3 cm.
03

Calculate the volume

Substitute the given values into the volume formula: \[ V = \pi (4)^2 (3) = 16 \pi (3) = 48 \pi \]. Compute the volume: \[ 48 \pi \approx 150.80 \text{ cm}^3\].
04

Calculate the surface area

Substitute the given values into the surface area formula: \[ SA = 2 \pi (4) (4 + 3) = 2 \pi (4) (7) = 56 \pi \]. Compute the surface area: \[ 56 \pi \approx 175.93 \text{ cm}^2 \].

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Key Concepts

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

Volume of a Cylinder
To find the volume of a cylinder, you need to understand the volume formula which is: \( V = \pi r^2 h \).
This formula tells us that you take the area of the base (which is a circle) and multiply it by the height of the cylinder.

Let's break it down step-by-step:
  • \

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