SolGeom and AnaGeom Eval
Thursday, June 17, 2021 9:34 AM
1. A prism with an altitude of 15 cm has an octagonal base inscribed in a square
with side 10 cm. Find the volume of the prism.
1. Find the volume of material needed to build a perimeter wall 10m x 20m
x0.30m thick if the wall is 1.50 m high.
1. Find the volume of the of the largest cube that can be cut in a sphere with
radius of 25.40 in.?
Eval Discussion Page 1
1. Valerie bought a balloon with a radius of 4 in. She wanted the balloon to be
bigger so she blew so she blew 2 big breaths of air into the balloon, each big
breath increased the balloon's radius by 1 in. Find the ratio of the current
volume of the balloon to the original volume of the balloon.
1. Find the largest volume of a rectangular pyramid with a square base and a
height of 22.50 cm that can be cut from a sphere with a 27 cm.
Eval Discussion Page 2
1. A pyramid has a square base 8 cm. in length and has an altitude of 20 cm.
The pyramid is cut by a plane parallel to the base. If the distance of the plane
from the base is 7 cm., determine the volume of the smaller pyramid.
1. Find the lateral area of a cone whose diameter is 12 cm. and whose height is
8 cm.
Eval Discussion Page 3
1. The longest slant height of an oblique circular cone, 4.5√3 ft. and the
shortest , 4.5 ft. subtends an angle of 30 degrees at the vertex of the cone.
What is the volume?
1. The internal radius of a pipe is 4 cm. and the external radius is 6 cm. If it has
Eval Discussion Page 4
1. The internal radius of a pipe is 4 cm. and the external radius is 6 cm. If it has
a length of 30 cm., find the total surface area.
1. A cylindrical vessel with open top has a total surface area of 49.48 sq. ft. If its
height is 1.5 times its diameter, determine the base diameter.
1. A water reservoir is shaped such that the top is a rectangle with sides 12 m.
and 30 m. while the bottom is also a rectangle with sides 8 m. and 20 m. If
the reservoir has a depth of 5 m. Find the capacity of the reservoir in liters.
1. The base diameters of a frustum of a right circular cone are 2 m. and 4 m. If
its altitude is 5 m., determine its lateral area.
Eval Discussion Page 5
1. Determine the distance between the points (2, 8) and (-1, 5).
1. Find the distance between the point (2, 5) and the line 4x-3y=-22.
1. Triangle ABC has the following coordinates: A (2,3), B (-2,-4) and C (6,-8). Find
the coordinates of the centroid.
1. Find the area of a quadrilateral ABCD with its vertices at A (4,10), B (10,8),
C(11,2) and D (2,2).
Eval Discussion Page 6
1. Find the slope of a line having an equation of 3x-2y+17=0.
1. What is the equation of a line which intercepts the y-axis at 4 and also
intercepts the x-axis at 3?
1. What is the slope of the line parallel to the line 4x-5y+9=0?
1. Determine the area of the triangle formed by the coordinate axes and the
line that passes through the point (2,3) with equal x and y intercepts.
Eval Discussion Page 7
1. Given the lines 3x+y-2=0 and 2x+by-6=0, find the value of b so that the two
lines form an angle of 45 degrees.
1. Find an equation of the line that bisects the angle between the lines 4x-3y-7=
0 and 5x+12y+8=0.
Eval Discussion Page 8
1. Find the equation of circle passing through the points (3,0), (5,-2) and (-4,-7).
Eval Discussion Page 9
1. Determine the equation of the radical axis of the circles x^2+y^2-10x-6y+18=
0 and x^2+y^2-4x+12y+31=0
1. Find the coordinates of the foci of the conic section defined by the equation :
9x^2 +25y^2 =225.
Remaining Q and A's for AnalGeom:
Eval Discussion Page 10
