# Sadie Adams

Geometry teacher | Verified Expert

Greetings! I'm a dedicated geometry expert, honing my skills at Loyola University Maryland. Passionate about shaping mathematical minds, I thrive on unraveling the complexities of geometry. With a commitment to fostering understanding, I'm here to guide students through the intricacies of shapes, angles, and the beauty of mathematical relationships. Let's embark on a journey of geometric exploration together!

## Questions

How do you find the maximum volume #V(theta, phi)# of the tetrahedron, with vertices at #(0, 0, 0), (cos theta, 0, 0), (0, sin theta, 0) and (cos theta, sin theta, cos phi)?#

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?

In a circle of diameter #40# cm, the length of a chord is #20# cm. Find the length of minor arc of the chord?

The area of a kite is 116.25 square feet. One diagonal measures 18.6 feet. What is the measure of the other diagonal?

Two corners of an isosceles triangle are at #(2 ,5 )# and #(4 ,8 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

What is the area of a parallelogram that has a 70 degree angle and sides with lengths 140 and 200?

How do you find the circumference of a circle with diamete of 33cm? Give your answer in terms of pi.

A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #3 # and the height of the cylinder is #5 #. If the volume of the solid is #20 pi#, what is the area of the base of cylinder?

Points A and B are at #(4 ,1 )# and #(8 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

A triangle has corners at #(6, 3 )#, ( 8, -2)#, and #(1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

What is the orthocenter of a triangle with corners at #(2 ,3 )#, #(6 ,1 )#, and (6 ,3 )#?

A triangle has corners A, B, and C located at #(3 ,1 )#, #(6 ,4 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Circle A has a center at #(8 ,5 )# and an area of #100 pi#. Circle B has a center at #(4 ,2 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/8 #, what is the difference between the areas of the rhombuses?

Circle A has a center at #(3 ,7 )# and a radius of #1 #. Circle B has a center at #(-3 ,3 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

How do you find the approximate area of an octagon given its diameter is 8 inches?

Two angles are supplementary. One angle is 5 degrees less than four times the other. What are the measures of the angles?

Two circles have the following equations: #(x -8 )^2+(y -5 )^2= 9 # and #(x +4 )^2+(y +2 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?