1. A container built in the shape of a cylinder has a circular base with a radius of 1.5
meters. The altitude of the container is 3.5 meters. How many cubic meters of fluid can
this container hold?
Base area = π r 2 = π (1.5 m ) ≈ 7.0686 m 2
2
Volume = Base area * Altitude
Volume = (7.0686 m2)(3.5 m) ≈ 24.74 m3
2. What is the total area of a right rectangular prism with a height of 8 feet, a width of 10
feet, and a thickness of 12 feet
Surface area = 2(Height * Width) + 2(Width * Thickness) + 2(Height * Thickness)
Surface area = 2(8 * 10) + 2(10 * 12) + 2(8 * 12)
Surface area = 2(80) + 2(120) + 2(96)
Surface area = 160 + 240 + 192
Surface area = 592 square feet
3. What is the total area of a right rectangular prism with a height of 10 feet, a width of 6
feet, and a thickness of 4 feet?
Surface area = 2(Height * Width) + 2(Width * Thickness) + 2(Height * Thickness)
Surface area = 2(10 * 6) + 2(6 * 4) + 2(10 * 4)
Surface area = 2(60) + 2(24) + 2(40)
Surface area = 120 + 48 + 80
Surface area = 248 square feet
4. A triangle that contains angles of 27°, 90°, and 63° is a(n) _______ triangle.
A triangle that contains an angle of 90º is a right triangle.
5. What is the volume of a frustum of a right pyramid with the area of the lower base
equal to 100 square inches, the area of the upper base equal to 25 square inches, and the
altitude equal to 12 inches?
Let A1 represent the area of the lower base, and let A2 represent the area of the
upper base.
The volume of the frustum is then given by:
(
1
Volume = h A1 + A2 + A1 * A2
3
)
With a height (altitude) of 12 inches, A1 = 100, and A2 = 25, the volume is:
Volume =
(
1
12in ) 100 in 2 + 25 in 2 + 100in 2 * 25 in 2
(
3
)
Volume = 700in 3
6. A monument in the form of a marble cylinder has a circular base with a radius of 1.5
meters. The altitude of the monument is 3.5 meters. How many cubic meters of marble
does this monument
This is effectively the same as the first problem, as both are concerned with a
cylinder of radius 1.5 m and a height of 3.5 m.
The volume of this monument will be the same: 24.74 m3
7. If a decorative sign in the form of a circle has a diameter of 10 feet, what is the area of
the sign, to the nearest square foot?
2
⎛ 10 ft ⎞
≈ 79 ft 2
Area = π r 2 = π ⎜
⎝ 2 ⎟⎠
8. A monument is made in the form of a right pyramid with a regular hexagon as a base.
Each base side is 5 meters and the slant height is 30 meters. If only the sides (and not the
base) of the monument is to be covered by metal, how many square meters of metal are
needed to cover the sides of the pyramid?
The area of each side will be:
1
1
( base side length )(slant length ) = ( 5 m )( 30 m ) = 75 m 2
2
2
Since there are 6 sides, the total area required to be covered are:
Total area = 6(75 m2) = 450 m2
9. Find the perimeter of an ellipse if the major axis is 30 millimeters (mm) and the minor
axis is 12 mm. Round off your answer to the nearest whole number
The perimeter of an ellipse is difficult to calculate. There are some approximate
formula, and a couple of exact solutions which involve infinite series.
Since the answer here is to be rounded to the nearest whole number, this
approximation should be sufficient:
p ≈ π ⎡ 3( a + b ) −
⎣
( 3a + b )( a + 3b ) ⎤⎦
where a is the length of the semi-major and b is the length of the semi-minor axis.
For this problem, a = 30/2 = 15 mm, and b = 12/2 = 6 mm
The approximate perimeter is then:
p ≈ π ⎡ 3(15 + 6 ) −
⎣
p ≈ π ⎡ 3( 21) −
⎣
p ≈ π ⎡ 63 −
⎣
( 3*15 + 6 )(15 + 3* 6 ) ⎤⎦
( 45 + 6 )(15 + 18 ) ⎤⎦
( 51)( 33) ⎤⎦
p ≈ 69.038
Rounded to the nearest whole number, the perimeter is 69 mm.
10. What is the altitude of a rhombus if it’s area is 10 square meters and the length on one
side is 2.5 meters?
The area of a rhombus is equal to the product of the length of the side and the
altitude.
For the given rhombus:
Area = (side)(altitude)
10 m2 = (2.5 m)(altitude)
altitude = 10 m2 / 2.5 m
altitude = 4 m
11. What is the total area of a right rectangular prism with a height of 8 feet, a width of
10 feet, and a thickness of 12 feet?
This is a repeat of problem #2.