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?