Accelerated Geometry
SAV Practice
Name
Per/Sec.
Date
1.
How many faces does an octagonal pyramid
have?
2.
If the radius of the base of a cylinder is 6 and
the height is 3 , find the volume.
3.
How many vertices does a hexagonal pyramid
have?
4.
Find the lateral area of the regular pyramid.
5.
Suppose a 3 -4-5 right triangle is revolved about
its shorter leg as an axis. Find the volume of the
solid.
6.
Find the area of a rhombus, if the length of the
diagonals are 4 and 1 0.
7.
Which of the following is a prism?
a)
b)
c)
8.
If the area of a rectangle is 1 00 and the ratio of
the length to the width is 4 : 1 , find the width.
d)
e)
Page 2
9.
Find the total surface area of a cylinder with
radius r = 8 in: and height h = 5 in.
1 0. A metal ball with a hollow, spherical core is cast
out of metal. The diameter of the hollow core is
8 in. and the ball' s outermost diameter is 1 0 in.
To the nearest tenth of a cubic inch, how much
metal was used to cast the ball?
1 1 . A triangle is inscribed in a semicircle. The
semicircle has an area of 1 8 . What is the area
of the inscribed triangle?
1 2 . A cube has an internal diagonal of length 1 2 .
What is the exact volume of the cube?
1 3 . Each side of the base of a regular triangular
pyramid measures 8 ft. The slant height makes
an angle of 45 with the altitude. Find the total
surface area of the pyramid. (Find your answer
to the nearest tenth. )
1 4. The altitude of a cone measures 2 0 units and the
slant height measures 2 5 units. Find the total
surface area.
1 5 . The silo shown is composed of a hemisphere
and a cylinder. The total height of the silo
is 2 0 meters and the diameter of the silo is
8 meters. What is the volume of the silo to the
nearest cubic meter?
1 6. If the volume of a cube is 8 m! , what is the
surface area?
Page 3
1 7 . In the diagram, a plane is passed through a
sphere at a point that is x units away from the
center of the sphere. The radius of the sphere
is y units. Express the cross-sectional area of
intersection in terms of x and y.
1 8. Eb' s king size waterbed is 2 . 2 meters long,
1 . 87 meters wide, and 2 5 . 65 centimeters thick.
If water weighs 2 2 03 . 63 5 lbs per cubic meter,
about how much does Eb' s bed weigh when it is
filled with water?
1 9. The following are dimensions of two right
circular cylinders. All have the same volume
.
AN?AFJ the one that has
2 0. An arc of a circle measures 45 . If the length of
the arc is 2 , what is the area of the circle?
a) r = 2 and h = 9
b) r = 2 and h = 1 8
c) r = 3 and h = 8
d) r = 6 and h = 2
e) r = 4 and h = 4 : 5
2 1 . The area of the square in the figure is 1 6. What
is the area of the shaded region?
2 2 . If the length of a rectangle is twice the width
and the area is 7 2 , find the width.
Page 4
2 3 . The bases of a prism are equilateral triangles
with sides measuring 6 ft, and the altitude
measures 3 ft. Find the volume.
2 4. A satellite is in orbit at a constant distance of
3 00 miles from a tracking station. It is tracked
through a 45 arc. How far, in miles, did the
satellite travel?
2 5 . If the dimensions of a rectangular prism are 4
by 2 by 3 , then the volume is
.
2 6. The shaded rectangle in the diagram was formed
by joining two diagonals of the regular hexagon
with two sides. If the side lengths of the hexagon
are 1 4 cm, what is the exact area of the shaded
rectangle?
2 7 . Which of the following is a polyhedron with two
congruent bases?
2 8. Find the lateral area of the right prism.
a)
b)
d)
e)
c)
Page 5
2 9. Which of the following is a cone?
a)
b)
d)
e)
c)
3 0. Find the lateral area of the right circular
cylinder.
3 1 . A regular hexagon has a perimeter of 1 2 0 ft.
What is the area of this hexagon?
3 2 . What is the diameter in feet of a wheel which,
when rotating at a speed of 1 0 revolutions per
minute, takes 1 8 seconds to travel 1 5 feet?
3 3 . The altitude of a cone measures 2 0 units and the
slant height measures 2 5 units. Find the total
surface area.
3 4. A cardboard tube is unrolled to form a rectangle
as shown. If the volume of the original tube was
2 00 and the height was 8, what is the area of
the rectangle?
3 5 . A pyramid has a square base with sides of length
4 and a height of 8. Find the volume of the
pyramid. (Round your answer to the nearest
tenth. )
3 6. A solid figure having congruent circular bases in
a pair of parallel planes is a
.
Page 6
3 7 . Find the
F surface area of a sphere whose volume
is 4 3 .
3 8. The area of square ABCD is 1 00 and the area
of square AGFE is 9. Find the area of square
HEBK.
3 9. How many sides of a triangular pyramid are
triangles?
40. The bases of a trapezoid measure 1 2 and 1 7 and
the height of the trapezoid is 5 . What is the area
of the trapezoid?
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