MATH SOLVE

3 months ago

Q:
# The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.1) What is the volume, in cubic centimeters, of the object? Explain how you found the volume of the (2) smaller shapes.2) Then explain how you found the volume of the total shape.**Do not just show your answer. Explain your steps and the numbers you used.**Did you use radius? height? diameter? base? Pi (3.14)?

Accepted Solution

A:

Answer:Part 1) The volume of the object is [tex]32\pi\ cm^{3}[/tex] or [tex]100.48\ cm^{3}[/tex]
Part 2) see the procedureStep-by-step explanation:The picture of the question in the attached figurePart 1) What is the volume, in cubic centimeters, of the object?we know thatThe volume of the object is equal to the volume of the cylinder plus the volume of the coneFind the volume of the coneThe volume of the cone is equal to[tex]V=\frac{1}{3}\pi r^{2} h[/tex]we have[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=3\ cm[/tex]substitute the values[tex]V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}[/tex]Find the volume of the cylinderThe volume of the cylinder is equal to[tex]V=\pi r^{2} h[/tex]we have[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=(10-3)=7\ cm[/tex]substitute the values[tex]V=\pi (2^{2})(7)=28\pi\ cm^{3}[/tex]Part 2) Then explain how you found the volume of the total shapeThe volume of the total shape is equal to the volume of the cylinder plus the volume of the cone[tex]4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}[/tex] ------> exact valueFind the approximate value of the volumeassume[tex]\pi=3.14[/tex][tex]32(3.14)=100.48\ cm^{3}[/tex]