Volumes 1
Trigonometry 1
Volume 2
Trigonometry 2
Any Regents Question
100
Name the following two figures 
Which family do they belong to: cylinder, prism, or pyramid?
100
What is the definition of the sine function?
input : angle
output : ratio
100
A plane intersects a cylinder perpendicular to its bases.
This cross section can be described as a
(1) rectangle (3) triangle
(2) parabola (4) circle
a horizontal cut or a vertical cut ?
100
Which expression is equal to sin 41°?
(1) tan 41° (3) cos 49°
(2) sin 49° (4) cos 41°
What do you know about cofunctions? How can calculators be useful?
100
On the set of axes below, triangleRST is the image of triangle ABC after a dilation centered at point P.
The scale factor of the dilation that maps triangle ABC onto triangle RST is
1) 1/3 2)2 3) 3 4) 2/3
How do you use image length and preimage length to determine the scale factor ?
200
Do they have the same volume ? Explain
How do you find volume of a cylinder or a cone ?
200
If two legs of a right triangle are 2 and 8, what is the length of the third side ?
what do you know about the legs and hypotenuse of a right triangle
200
In the diagram below, a sphere is inscribed inside a cube. The cube has edge lengths of 18.
What is the volume of the sphere, in terms of π?
(1) 108π (2) 972π (3) 432π (4) 7776π
What is the radius of the sphere ?
200
what is the length of AB ?
Which function can help us to find the missing side? SOH , CAH , TOA
200
Which regular polygon has a minimum rotation of 36° about its center that carries the polygon onto itself?
(1) pentagon (2) nonagon (3) octagon (4) decagon
What is the formula for finding the minimum angle of rotation of a polygon?
300
A tent is in the shape of a right pyramid with a square floor. The square floor has side lengths of 8 feet. If the height of the tent at its center is 6 feet, what is the volume of the tent, in cubic feet?
1) 48 2) 128 3) 192 4) 384
What does a right square pyramid look like?
300
In the diagram of triangle ABC below, m∠C 90°, CB=13, and AB= 16.
What is the measure of ∠A, to the nearest degree?
(1) 36° (2) 51° (3) 39° (4) 54°
What will be helpful? trig functions or their inverse functions ?
300
The Pyramid of Memphis, in Tennessee, stands 107 yards tall and has a square base whose side is 197 yards long
What is the volume of the Pyramid of Memphis, to the nearest cubic yard?
(1) 751,818 (2) 2,076,212
(3) 1,384,188 (4) 4,152,563
How do you find the volume of a square pyramid ?
300
Triangle ABC has a right angle at C. If AC = 7.7 and m/B 5 = 24°, what is AB, to the nearest tenth?
(1) 18.9 (2 ) 8.4 (3) 17.3 (4) 3.1
How could trigonometry be useful in finding the missing side?
300
Which information is sufficient to prove that triangle BXY ∼ triangle BAC?
what are the different ways to show triangles are similar ? AA similarity Thm
SAS similarity Thm
SSS similarity Thm
400
The pyramid shown below has a square base, a height of 7, and a volume of 84.
What is the length of the side of the base?
1) 6 2) 12 3) 18 4) 36
What is the formula to find the volume of pyramid / a square pyramid ?
400
Kayla was cutting right triangles from wood to use for an art project. Two of the right triangles she cut are shown below.If ABC ∼ DEF, with right angles B and E, BC =13 cm, and AC =29 cm, what is the measure of ∠F, to the nearest degree?
(1) 78° (2) 62° (3) 63° (4) 88°
What do you know about angles in similar triangles?
400
A rectangle with dimensions of 4 feet by 7 feet is continuously rotated about one of its 4-foot sides. The resulting three-dimensional object is a
(1) cylinder with a height of 7 feet and a base radius of 4 feet.
(2) cylinder with a height of 4 feet and a base radius of 7 feet.
(3) cone with a height of 7 feet and a base radius of 7 feet.
(4) cone with a height of 4 feet and a base radius of 7 feet.
Would a graph be useful ?
400
In RST below, RS = 9 cm, RT = 8 cm, and m∠TRS = 55°.What is the area of RST, to the nearest square centimeter?
1) 59 2) 36 3) 29 4) 21
What is formula of finding triangle area using sine ?
400
In the diagram below of right triangle BAL, altitude AD is drawn to hypotenuse BL. The length of AD is 6. If the length of DL is four times the length of BD, determine and state the length of BD.
Can we apply the object -shadow theorem here?
500
A storage building is modeled below by a hemisphere on top of a cylinder. The diameter of both the cylinder and hemisphere is 12 feet. The total height of the storage building is 30 feet.
To the nearest cubic foot, what is the volume of the storage building?
1) 942 2) 3167 3) 2488 4) 3845
What different solids do you see in this composite figure?
500
Line segment PAQ has endpoints whose coordinates are P(-2,6) and Q(3,-4). What are the coordinates of point A, such that PA:AQ =2:3?
(1) (1,0) (2) (-1,4) (3) (2,-2) (4) (0,2)
Which approach would you prefer: graphing a right triangle or using algebra to find the answer?
500
In right triangle MTH shown below, m∠H = 90°, HT = 8, and HM= 5.
Determine and state, to the nearest tenth, the volume of the three-dimensional solid formed by rotating triangle MTH continuously around MH.
what solid do you get by rotating triangle MTH continuously around MH ?
500
In a right triangle, the acute angles have the relationship sin(3x − 7)° = cos(x + 1)°. Determine the measure of the smaller angle.
Is the unknown x part of the angle or part of the value?
500
If EA = 7.2, EJ = 9, AJ = 5.4, and HM =3.29, what is the length of MJ, to the nearest hundredth?
(1) 2.47 (2) 4.11 (3) 2.63 (4) 4.39
How can you set up a proportion for the two similar triangles?