Select all shapes that have a volume of36 π. **Understanding the Dimensions of a Cone**In the image, we see a right circular cone. The essential characteristics of this cone are clearly depicted with the following measurements:- **Height (h):** The perpendicular distance from the base to the apex (top) of the cone is $12$ units.- **Radius (r):** The radius of the base of the cone, which is the distance from the center of the base to any point on its circumference, is $3$ units.### Diagram Explanation:The cone is illustrated in a two-dimensional diagram. A dashed line represents the height of the cone, running vertically from the base to the tip. The radius is marked as extending horizontally from the center to the edge of the base, forming a right angle with the height.**Option:**- Option 5**Next Steps:**To further explore this cone, you could calculate various properties such as the volume and surface area. Use the following formulas:- **Volume (V) of a cone:** \[ V = \frac{1}{3} \pi r^2 h \]- **Surface Area (A) of a cone:** \[ A = \pi r (r + \sqrt{h^2 + r^2}) \]Where $ \pi $ (Pi) is approximately $ 3.14159 $.In our example:- $ r = 3 $- $ h = 12 $By substituting these values into the formulas, you can find the specific volume and surface area of the cone depicted in the diagram. ### Volume Selection Exercise**Instructions:**Select all shapes that have a volume of 36π.#### Options:**Option 1: Cone**- Diagram: A cone with a height of 6 units and a radius of 6 units.- Volume Formula: $\frac{1}{3}\pi r^2 h$**Option 2: Triangular Prism**- Diagram: A prism with a triangular base, height of 3 units, base length of 4 units, and a width of $3\pi$ units.- Volume Formula: $\frac{1}{2} \times \text{Base length} \times \text{Height} \times \text{Prism length}$**Option 3: Rectangular Prism**- Diagram: A rectangular prism with dimensions 3 units $\times$ $3\pi$ units $\times$ 4 units.- Volume Formula: $ \text{Length} \times \text{Width} \times \text{Height}$**Option 4: Pyramid**- Diagram: A pyramid with a square base of side length 4 units and height of 3 units. The pyramid height is 3 units.- Volume Formula: $\frac{1}{3} \times \text{Base Area} \times \text{Height}$**Calculations and Explanations:**1. **Option 1: Cone** - Calculate the volume: $\frac{1}{3}\pi \times 6^2 \times 6 = 72\pi$ - The volume is 72π, not 36π.2. **Option 2: Triangular Prism** - Calculate the volume: $\frac{1}{2} \times 4 \times 3 \times 3\pi = 18\pi$ - The volume is 18π, not 36π.3. **Option 3: Rectangular Prism** - Calculate the volume: $3 \times 4 \times 3\pi = 36\pi$ - The volume is 36π.4. **Option 4: Pyramid** - Calculate the volume: $\frac{1}{3} \times (4^2) \times 3 = 16$ - The volume is 16, not including

Name: Select all shapes that have a volume of36 π. **Understanding the Dimen
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Select all shapes that have a volume of36 π. **Understanding the Dimensions of a Cone**In the image, we see a right circular cone. The essential characteristics of this cone are clearly depicted with the following measurements:- **Height (h):** The p

Solid cone volume of a solid cone = (⅓)πr2h Solid rectangle volume of solid rectangle =…

Answered: Select all shapes that have a volume of…

Math

Geometry

Select all shapes that have a volume of 36 π.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.13: Using Factoring To Solve Problems

Problem 27P

See similar textbooks

Related questions

Q: Find the volume of a sphere formula

A: To Find the volume of a sphere formula The volume of the disc element, dV can be expressed by:

Q: A monoply box that has twice the the awichth me twice the length with a volume of 10000 cm³ Find the…

Q: The cube in the figure has an edge of 10 cm. Calculate the volume of the vertex BCDG tetrahedron and…

Q: 2 ft 3 ft 4 ft

Q: Each hemisphere of a beach ball has a volume of 281,250 cm³. What is the radius of the ball, in cm?

A: given volume of hemisphere is 281250π cm3

Q: Find the volume of the unit sphere.

Q: Find the exact volume of the largest cube that would fit inside a hollow cylinder. The cylinder has…

Q: Find the volume of each figure

Q: Suppose the volume of a given sphere is 24429cm³. Find the size of area of the spherical triangle…

A: There appears to be two questions. The first question carries a figure and some information, but no…

Q: A composite figures form by placing half-sphere atop a cylinder. The half-sphere and the cylinder…

A: Solving the following problem

Q: Find the volume of the solid. The volume is cubic units.

A: solution

Q: Find the volume of a right triangular prism whose height is 4 and base is a right triangle with legs…

A: Find the area of base and then multiply the area with height.

Q: Find the volume of the hollow sphere

Q: Find the volume of the hollow birdhouse

A: The hollow bird house is a combination of a cuboid with the length of its edges equal to 7 in, 7 in,…

Q: A paper drinking cup in the shape of a cone has a height of 10 centimeters and a diameter of 8…

Q: If 1,200 cm2 of material is available to make a box with a square base and an open top, find the…

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

Select all shapes that have a volume of

36 π.

**Understanding the Dimensions of a Cone**

In the image, we see a right circular cone. The essential characteristics of this cone are clearly depicted with the following measurements:

- **Height (h):** The perpendicular distance from the base to the apex (top) of the cone is $12$ units.
- **Radius (r):** The radius of the base of the cone, which is the distance from the center of the base to any point on its circumference, is $3$ units.

### Diagram Explanation:

The cone is illustrated in a two-dimensional diagram. A dashed line represents the height of the cone, running vertically from the base to the tip. The radius is marked as extending horizontally from the center to the edge of the base, forming a right angle with the height.

**Option:**
- Option 5

**Next Steps:**

To further explore this cone, you could calculate various properties such as the volume and surface area. Use the following formulas:

- **Volume (V) of a cone:**
\[ V = \frac{1}{3} \pi r^2 h \]
- **Surface Area (A) of a cone:**
\[ A = \pi r (r + \sqrt{h^2 + r^2}) \]

Where $ \pi $ (Pi) is approximately $ 3.14159 $.

In our example:
- $ r = 3 $
- $ h = 12 $

By substituting these values into the formulas, you can find the specific volume and surface area of the cone depicted in the diagram.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

A cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of the container.
pyramid 3 m high has a square base that is 3 m on a side. The crosssection of the pyramid perpendicular to the altitude x meters down from the vertex is a square x meters on a side. Find the volume of the pyramid.
How do I set up? Approximate the area of a regular pentagon of radius 4 cm.
the length of a rectangular piece of cloth to be placed in the rattan table is 2 m more than its width. if the area of the cloth is 120m^2, find the width
MÁT Geometry_S21 A https://testing.illuminateed.com/assessment/60957cbdb5fa09c25e8b5706/609dd505db37477a078b54dc/1?rldbqn=1 12. What is the volume of a square pyramid with height 15m and slant height 17m? A 85 m2 B 320 m2 C 1280 m2 D 3840 m2 GO ON [7] 021 Illuminate Education TM, Inc. DELL F1 F2 F3 ES F6 F7 F8 F9 F10 F11 8.
determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 316.5 square centimeters find height length and width in cm
A solid consists of a pyramid with a slant height of 39 cmn attached to a cuboid with absquare base of sides 30 cm and a height of 70 cm. Find (i) the volume, (ii) the total surface area, of the solid.
Q3/ The surfaces p = 3, p= 5, p = 100, p = 130, z= 3, and z= 4.5 define a closed surface. Find (a) the enclosed volume; (b) the total area of the enclosing surface; (c) the total length of the twelve edges of the surfaces; (d) the length of the longest straight line that lies entirely within the volume.
There is a [Emerald Jade] Mazu altar 8m*6m, the elevation of the completed RC surface (cm) is as followsThe grid size is 100cm * 100cmIf the coordinate points are highly convex, they need to be removed.It is required that the slopes of two consecutive squares [east-west direction, north-south direction] must be less than 2%The cost of coordinate grid removal is 10,000 yuan per centimeter.Plan your excision plan, total cost =?[A] 50,000 yuan for erecting a grinding machine at each point, calculate the total cost
I'm having touble depicting how tall, how wide, where’s the start, and which way does it point. I appreciate your help.
Hi! can someone please help me with number 4 please and thank you.