Geometry Questions

3 Calculate the volume of a pyramid with a base area of 10cm and a height of 5cm

4 Calculate the surface area of a cylinder with a radius of 3m and a height of 12m Leave your answer in terms of WA

2 Calculate the volume of a prism with a base area of 45ft2 and a height of 2ft

1 A rectangular prism fish tank is filled with 677 cm of water and has some colorful pebbles at the If the base of the tank has an area of 40cm and the height of the tank is 20 cm determine the volume of the pebbles in the tank a 123 cm b 1477 cm c 800 cm 3 to allo smulov se snimned 25

3 Determine whether you would need to add or subtract to find the volume of the complex figures below a ADD SUBTRACT What two shapes would you find the volume of b 12 in ADD 13 in SUBTRACT What two shapes would you find the volume of

1 Determine the surface area of a cylinder with a diameter of 10 in and a height of 4 in Round to the nearest tenth Draw the figure first

An interior angle of a regular polygon has a measure of 108 What type of polygon is it pentagon O hexagon O octagon O nonagon

he regular octagon has a perimeter of 122 4 cm 20 cm Y W Which statements about the octagon are true Select two options The length of segment YZ is 15 3 cm O The measure of the angle formed by the radius and the apothem is 30 O The length of segment XY can be found by solving for a in 20 7 65 a O The length of segment WZ is 20 cm The measure of the central angle ZZXW is 45

A regular heptagon has a radius of approximately 27 87 cm and the length of each side is 24 18 cm What is the approximate area of the heptagon rounded to the nearest whole number Recall that a heptagon is a polygon with 7 sides O 1 173 cm O2 125 cm O2 359 cm D

Galina is finding the area of triangle RST To do so she follows the steps in the table Step Draw a rectangle around triangle RST Step Find the area of the rectangle 2 Step 3 Find the area of the three right triangles created by the sides of the rectangle and the intersection with each vertex of the triangle Step Subtract the area of the right triangles from the area of the rectangle To solve the problem using these steps what are the dimen ns of the rectangle she should draw R 5 3 2 5 4 3 2 1 24 3 5 S O2 units by 4 units 3 units by 4 units 19 F Funits T 3 4 5 X

To find the area of parallelogram RSTU Juan starts by drawing a rectangle around it Each vertex of parallelogram RSTU is on a side of the rectangle he draws U 3 3 2 1 w 4 T S X Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU O 2 18 4 18 4 O 18 4 O 18 4

Four interior angles of a pentagon measure 88 118 132 and 100 What is the measure of the fifth interior angle 82 O 92 O 102 O 112

A regular pentagon is shown 9 4 cm 8 cm What is the length of the apothem rounded to the nearest tenth 2 9 cm 3 3 cm 4 9 cm 6 5 cm

A regular octagon has an apothem measuring 10 in and a perimeter of 66 3 in 10 in What is the area of the octagon rounded to the nearest square inch O88 in O 175 in O 332 in O 700 in

A square has an apothem measuring 2 5 cm and a perimeter of 20 cm What is the area of the square rounded to the nearest square centimeter O 13 cm O 25 cm O 50 cm O 100 cm

A regular hexagon is shown 12 in b C What is the measure of the radius c rounded to the nearest inch Use the appropriate trigonometric ratio to solve O 6 in O 10 in 14 in O24 in

The base of the right triangle drawn in the regular octagon measures 0 7 cm 1 9 cm 0 7 cm What is the perimeter of the octagon 11 2 cm 14 1 cm O 15 2 cm 20 8 cm

The area of the regular hexagon is 169 74 ft2 7 ft What is the perimeter rounded to the nearest tenth O 24 2 ft 28 3 ft O 48 5 ft O 56 8 ft

Bianca calculated the height of the equilateral triangle with side lengths of 10 tan 30 h 8 7 h A 30 Then she used the formula for area of a triangle to approximate its area as shown below bh 10 8 7 43 5 units2 5 Calculate the area of the equilateral triangle using the formula for area of a regular polygon and compare it to Bianca s answer The apothem rounded to the nearest tenth is units The perimeter of the equilateral triangle is Therefore the area of the equilateral triangle is or approximately 43 5 units V The calculated areas are units

Manuel wants to buy a window shade to cover the window and frame shown The window is in the shape of a regular octagon The radius of the window including the frame is 2 ft and the measure of each edge of the octagonal frame is 1 52 ft Window 1 52 ft What is the approximate area of the window that nee to be covered including the frame O2 ft O 7 ft O 11 2 ft O22 5 ft

A community pool that is shaped like a regular pentagon needs a new cover for the winter months The radius of the pool is 20 10 ft The pool is 23 62 ft on each side To the nearest square foot what is the area of the pool that needs to be covered O192 ft O 960 ft O 1 921 ft 3 842

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21 8 cm 3 cm What is the area of the pentagon rounded to the nearest tenth O 13 8 cm O 17 3 cm O 32 7 cm O 69 0 cm

A hexagon has a radius measuring 23 cm What is the approximate area of the hexagon O 686 6 square cm O 793 5 square cm O 1374 4 square cm O 1587 0 square cm

A regular pentagon has a perimeter of 60 cm B A D What is the measure of angle CBD What is the length of segment CD cm Which trigonometric ratio can be used to compare Bo to CD using angle CBD What is the approximate length of BC cm What is the approximate length of BD GM

Probability and Counting 6 A fair die is rolled once Let A be the event of rolling a number less than 4 Let B be the event of rolling an even number A 4 1 Draw a Venn diagram 2 What is the probability of event A P A 3 What is the probability of event B P B 4 What is the probability of A and B P AnB 5 What is the probability of A or B P AUB

The floor of a gazebo is in the shape of a regular octagon The perimeter of the floor is 72 feet The distance from the center of the octagon to one of the vertices is 11 8 feet What is the approximate length of the apothem 3 feet What is the approximate area of the floor of the gazebo square feet 3

The pentagon below has an area of 8 3 square centimeters 2 2 cm What is the approximate length of the apothem O 0 4 cm O 0 8 cm O 1 5 cm O 1 9 cm

The radius of a regular decagon a 10 sided figure is 15 units The length of one side of the polygon measures about 9 3 units What is the approximate area of the regular decagon rounded to the nearest tenth O273 6 square units 0547 3 square units 663 1 square units 1069 9 square units

The area of the octagon below is 10 391 9 square millimeters 56 mm What is the approximate perimeter of the octagon Round to the nearest whole number mm What is the approximate length of one side of the octagon Round to the nearest whole number mm

The polygon below is a regular hexagon 18 cm 18 cm What is the approximate length of the apothem Rou to the nearest tenth O9 0 cm O 15 6 cm 20 1 cm 25 5 cm 0

A regular pentagon has an apothem measuring 20 cm and a perimeter of 145 3 cm 20 cm What is the area of the pentagon square centimeters

The sum of all but one interior angle of a heptagon is 776 What is the measure of the final interior angle O 42 O 56 O 124 304

What is the sum of the measures of the interior angles of a 12 gon O 1620 O 1800 O 1980 O 2160

77 66 59 62 12x What is the value of x O 6 O 8 O 10 O 12

Use circle J 5x 15 K 120 L J What is the value of x

2 Find an equation for the plane that contains the line in the ry plane y 2r 1 and the point 3 2 2

Consider the plane that contains the three points p 2 3 8 q 6 8 4 r 9 4 3 using p as your reference point write the equation of the plane in the form ax by cz d and state the value of d

In the circle below suppose m GHE 122 and m ZHGF 68 Find the following a m2GHE b mZHEF 0 X

6 5 4 3 2 6 5 4 3 2 1 2 3 4 6 The graph above is a transformation of the function x Write an equation for the function graphed above

10 5 4 3 2 6 5 4 3 2 1 2 3 5 1 2 3 4 5 2 The graph above is a transformation of the function Write an equation for the function graphed above

merry go round is rotating at the constant angular speed of 4 3 RPM counterclockwise The platform of this ride is a circular disc of radius 26 feet You jump onto the ride at the location picture elow Impose coordinates as pictured with units in feet a If 31 then what are your xy coordinates after 3 minutes Round your answers to three decimal places x y rotating 4 3 RPM b If 15 then what are your xy coordinates after 15 minutes Round your answers to three decimal places x y c If e x y jump on here X 11 then what are your xy coordinates after 8 seconds Round your answers to three decimal places

4 Find m A C 8 cm B 105 32 cm 14 A

7 2 PQRS is a parallelogram S ST and P 120 O DO

Type the inverse of the matrix Use decimals If no inverse exists type none 1 32 5 5

d If 8 2 1 rad then what are your xy coordinates after 2 hours and 6 seconds Round your answers to three decimal places x y Draw an accurate picture of the situation end start end start end start

A 101 1 10 101 101 110 110 b 2 2 4 12 5 2 SOXXB The general least squares solutions of Ax b for the given matrix A and vector b are all vectors of the form x Simplify your answers x with x

1 Given the two functions f x x 4x 1 and g t 1 t a Find and simplify f g 4 b Find and simplify g f x c Find and simplify f x g x

4 a Draw the area 9x y 9z 18x 4y 18z 32 0 b In a spherical coordinate system draw the area p sin2 cos 20 2 cos

4 Consider the matrix equation Ax b where a b A 1 1 1 where a b 0 a When is A strictly diagonally dominant and what does this tell us about the Gaus Seidel method for Ax b 1 marks b Find the iteration matrix for the Gauss Seidel method applied to Ax b 5 marks c Using your previous answers for what values of a and b does the Gauss Seidel metho 4 marks converge

1 Draw an SVAJ diagram 2 Find the coordinates of Q at q p 2 p and 3p 2 However Rb 1m W S 0 0 1 2 YA Rb base circle sin 20 S 0 2 2 0 1 2 sin 20 Efl m