T or F: Trigonometry is the study of three-dimensional objects

false

T or F: Volume is a cubic measure

true

T or F: a cube has eight contruent faces

false (it has 6)

T or F: the Pythagorean formula is c^{2} = a + b

false

the slant height is used to find the volume of a square pyramid

false

T or F: the hypotenuse is opposite the right angle in a right triangle

true

T or F: one cubic foot is equal to 144 cubic inches

false

T or F: the sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse

true

T or F: a cylinder is a type of prism

false

the tangent of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse

false

Identify the following shapes:

sphere, rectangular prism, cone, cylinder, pyramid

You will answer these using a trigonometric chart:

sin 60^{o}

cos 25^{o}

tan 58^{o}

cos 13^{o}

tam 42^{o}

.866

.906

1.600

.974

.900

volume of a cube

V = e^{3}

volume of a cone

V = 1/3pir^{2}h

Pythagorean Rule

c^{2} = a^{2} + b^{2}

sine of an angle

length of opposite leg

_________________

length of hypotenuse

volume of a square pyramid

V = 1/3lwh

cosine of an angle

length of adjacent leg

_________________

length of hypotenuse

volume of a rectangular prism

V = lwh

tangent of an angle

length of opposite leg

________________

length of adjacent leg

volume of a cylinder

V = pir^{2}h

Answer about a right triangle with sides of 3 ft & 4 ft.:

the length of the hypotenuse

c^{2} = a^{2} + b^{2}

c^{2} = 9 + 16 = 25

c = 5

Answer about a right triangle with sides of 3 ft & 4 ft.:

tangent of angle C =

sine of angle B =

cosine of angle B =

cosine of angle C =

tangent of angle B =

tangent of angle C = 3/4 = .750

sine of angle B = 4/5 = .800

cosine of angle B = 3/5 = .600

cosine of angle C = 4/5 = .800

tangent of angle B = 4/3 = 1.333

find the surface area of a cylinder that has a radius of 4 inches and a height of 18 inches.

SA = 2pirh + 2pir^{2}

SA = 2(3.14)(4)(18) + 2(3.14)(4^{2})

SA = 452.16 + 100.48

SA = 552.64 sq. in.

find the volume of a cone that has a 2 inch radius and a height of 6 inches

V = 1/3pir^{2}h

V = 1/3(3.14)(2^{2})(6)

V = 25.12 cu. in.

find the volume of a cylinder if the radius is 5 in. and height is 20 in.

V = pir^{2}h

V = 3.14(5^{2})(20)

V = 1570 cu. in.

find the volume of a square pyramid that has a 15 ft. square base and a height of 9 ft.

V = 1/3lwh

V = 1/3(15)(15)(9)

V = 675 cu. ft.

find the volume of a rectangular prism that is 20 ft x 10 ft x 5 ft

V = lwh

V = 20(10)(5)

V = 1000 cu. ft.

find the volume of a cone that has a 6 in. radius and a height of 15 in.

V = 1/3pir^{2}h

V = 1/3(3.14)(6^{2})(15)

V = 565.2 cu. in.

find the volume of a square pyramid that has a 10 in. square base and a height of 21 in.

V = 1/3lwh

V = 1/3(10)(10)(21)

V = 700 cu. in.

find the volume of acube wih 10 in edges

V = e^{3}

V = 10^{3}

V = 1000 cu. in.

find the volume of a rectangular prism that is 14 ft x 9 ft x 10 ft

V = lwh

V = 14(9)(10)

V = 1260 cu. ft.

find the volume of a cylinder if the radius is 1 ft. and the height is 4 ft.

V = pir^{2}h

V = 3.14(1^{2})(4)

V = 12.56 cu. ft.