/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Find the volume of the cone. A... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 9

Find the volume of the cone. A cone has a diameter of 11.5 inches and a height of 15.2 inches.

Short Answer

Expert verified
The volume of the cone is approximately 502.65 cubic inches.

Step by step solution

01

Calculate Radius

The radius of a cone is half the diameter, thus: \[r = \frac{d}{2}\], where d is the diameter. Substituting 11.5 inches for the diameter, the radius \(r = \frac{11.5}{2} = 5.75\) inches
02

Substitute into the Volume Formula

Next, substitute the radius of 5.75 inches and height of 15.2 inches to the formula \[V = \frac{1}{3} \pi r^2 h\], which yields that \[V = \frac{1}{3} \pi (5.75)^2 \times 15.2\]
03

Calculate the Volume

Perform the calculations within the formula to determine the volume of the cone. The volume is approximately = 502.65 cubic inches.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Geometry Formulas
Understanding geometry formulas is essential in solving problems related to shapes, including cones. For a cone, we focus on the volume formula which tells us how much space is inside the cone.
The formula for the volume of a cone is \[ V = \frac{1}{3} \pi r^2 h \]where:
  • \( V \) is the volume of the cone
  • \( r \) is the radius of the base of the cone
  • \( h \) is the height of the cone
  • \( \pi \) is a mathematical constant approximately equal to 3.14159
This formula is crucial because it helps convert the physical dimensions of a cone into a numerical value representing its volume, offering insight into its size in three-dimensional space. Understanding each part of the formula allows one to accurately calculate volumes with ease.
Cone Measurement
Measuring a cone involves determining its key dimensions: radius and height. These measurements are critical because they are inputs for the volume formula.
The radius of a cone is half the diameter of its base. In mathematical terms, given the diameter \( d \), the radius \( r \) is calculated as \( r = \frac{d}{2} \). In our example, with a diameter of 11.5 inches, the radius is:
  • \( r = \frac{11.5}{2} = 5.75 \) inches
The height \( h \) is the perpendicular distance from the base to the tip of the cone. For our cone, the height is given as 15.2 inches.
Measuring these dimensions accurately is essential because even small errors can lead to incorrect volume calculations.
Calculation of Volume
To calculate the volume of a cone, we use the formula for volume \( V = \frac{1}{3} \pi r^2 h \). Once you have the radius and height measurements, substitute them into the formula.
From our previous calculations:
  • Radius, \( r = 5.75 \) inches
  • Height, \( h = 15.2 \) inches
Substitute these into the formula:\[V = \frac{1}{3} \pi (5.75)^2 \times 15.2\]Calculate \( (5.75)^2 = 33.0625 \), then multiply by 15.2 to get the product 502.65, and finally multiply by \( \frac{1}{3} \pi \). This will give the approximate volume of the cone as 502.65 cubic inches.
This process illustrates how geometry formulas and measurement practice work together to determine the volume of a cone accurately.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the indicated measure. diameter of a circle with an area of 676\(\pi\) square centimeters

CRITICAL THINKING The height of cylinder X is twice the height of cylinder Y. The radius of cylinder X is half the radius of cylinder Y. Compare the volumes of cylinder X and cylinder Y. Justify your answer.

PROBLEM SOLVING You drop an irregular piece of metal into a container partially filled with water and measure that the water level rises 4.8 centimeters. The square base of the container has a side length of 8 centimeters. You measure the mass of the metal to be 450 grams. What is the density of the metal?

Find the surface area of the right cone. A right cone has a diameter of 11.2 feet and a height of 9.2 feet.

MATHEMATICAL CONNECTIONS You drill a circular hole of radius r through the base of a cylinder of radius R. Assume the hole is drilled completely through to the other base. You want the volume of the hole to be half the volume of the cylinder. Express r as a function of R.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.