# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

The diameter of two cylinder are in the ratio of 2:3. What will be the ratio of their heights if their volumes are equal ?

A line segment has endpoints at #(1 ,4 )# and #(4 , 9)#. The line segment is dilated by a factor of #1/3 # around #(4 , 2)#. What are the new endpoints and length of the line segment?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #7 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?

A triangle has angles of #78°#, #47°#, and #x+65°#. What is the value of #x#?

The base of a triangular pyramid is a triangle with corners at #(6 ,3 )#, #(4 ,7 )#, and #(8 ,8 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

A circle has a chord that goes from #( 3 pi)/4 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #81 pi #, what is the length of the chord?

A line segment goes from #(2 ,5 )# to #(3 ,2 )#. The line segment is dilated about #(5 ,4 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-2#, in that order. How far are the new endpoints form the origin?

If a circle has a circumference of 10 pie what is the circle's diameter?

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #2 #, #1/3 #, and #3 #, respectively. What is the rectangle's area?

The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(2 ,4 )#, and #(4 ,7 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

Two corners of an isosceles triangle are at #(5 ,4 )# and #(9 ,2 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

Is every rectangle a rhombus?

Circle A has a radius of #2 # and a center at #(8 ,3 )#. Circle B has a radius of #3 # and a center at #(3 ,2 )#. If circle B is translated by #<-2 ,6 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Two corners of an isosceles triangle are at #(4 ,8 )# and #(5 ,3 )#. If the triangle's area is #5 #, what are the lengths of the triangle's sides?

An ellipsoid has radii with lengths of #14 #, #4 #, and #6 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #12 # and the height of the cylinder is #4 #. If the volume of the solid is #16 pi#, what is the area of the base of the cylinder?

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #15 #, #8 #, and #7 #, respectively. What is the rectangle's area?

What is the centroid of a triangle with corners at #(1 , 1 )#, #(6 , 2 )#, and #(2 , 5 )#?

The base of a triangular pyramid is a triangle with corners at #(1 ,4 )#, #(6 ,2 )#, and #(8 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

How many lines of symmetry does a parallelogram have?