3D Geometry Questions and Answers

Find the surface area of the cone to the nearest whole number Hint Use the Pythagorean Theorem to find the slant height Note Diameter 10 cm 12 cm 10 cm Select one O a 267 cm O b 691 cm O c 723 cm O d 283 cm

Find the surface area of the pyramid round to the nearest whole number Hint The base is a regular hexagon with side length 10 m and apothem 5 3 m Remember the area of a regular polygon is equal to 1 2 pa where p is the perimeter of the base and a is the apothem 5 3 m 10 m l 10 m Select one O a 467 square meters O b 300 square meters O c 560 square meters O d 250 square meters

Find the volume of the triangular prism described below The base is a 45 45 90 triangle with a leg of 8 in The height is 1 6 in The volume of the prism is in Type an integer or a decimal

Find the volume of the triangular prism to the right The volume of the prism is ft Type an integer or a decimal 3 ft

18 A 16 cm 3 cm Complete the chart below 3D Figure 6 ini 8 in A 12 cm 5 cm 7 in 20 cm 10 cm 11 cm Name Horizontal Cross Section Drawing Vertical Cross Section Drawing Horizontal Cross Section Name C

Determine the volume of packing peanuts needed to fill the box if the radius of the enclosed cylinder is 4 centimeters and the cylinder is centered in the box 18 cm 28 cm 12 cm 8 cm

If sewage passes through the connector hole so that half of the volume contains sewage how much sewage fills the hole

the 3D figure by the most specific name Name the horizontal cross section Name the vertical cross section Draw the horizontal cross section below 71 F K G J H E Draw the vertical cross section below D A C B

Horizontal Cross Section Drawing Name Vertical Cross Section Drawi Intel 1 i

3 What 3D shape would be formed if you rotated the figure below 360 degrees around the x axis LO 5 0 a Cone b Triangular Prism c Triangular Pyramid 2

7 Find the volume of the given prism Round to the nearest tenth if necessary 6 4 cm 4 8 cm 11 5 cm Not drawn to scale

6 Which object is formed when right triangleKST is rotated around leg RS a A pyramid with a square base b An isosceles triangle c A right triangle ng R d A cone S

The scale factor of the dimensions of two similar wood floors is 3 2 It costs 60 to refinish the smaller wood floor At that rate how much would it cost to refinish the larger wood floor Simplify your answer

Using Cavalieri s Principal what is true when comparing the following three solids c D A B If they have the same height they have the same volume If they have the same cross sectional area at any given level they have the same volume If their cross sectional areas are the same at any given level and their heights are the same they have the same volum If their cross sectional areas are the same at any given level and heights are the same they have the same surface a

When graphing the polar equation r 3 cos 20 as moves from 3 to the radius changes from 0 graph is in quadrant to 3 and the

Identify two chords A D B C DE and FG FG and HI DF and EG DE and HI

A right circular cylinder is shown below B Which of the following could be a two dimensional figure that results when a plane intersects this right circular cylinder Select three that appl A circle C 80 cm D ellipse triangle 60 cm rectangle

Rectangle JUST has coordinates J 1 15 U 8 15 S 8 9 T 1 9 What is the perimete of rectangle JUST

A sphere with a radius of 2 5 feet

Which statements are true regarding the relationships between central inscribed and circumscribed angles of a circle Check all that apply A circumscribed angle is created by two intersecting tangent segments O A central angle is created by two intersecting chords that are not a diameter The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc O The measure of a central angle will be half the measure of an inscribed angle that intercepts the same arc O The measures of a central angle and circumscribed angle that intercept the same arc will sum to 90 The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle

am How do we know that alleles actually separate during gamete formation A Scientists are unsure whether the alleles separate B Zygotes will not reach maturity if the alleles do not separate C If the alleles did not separate recessive alleles would never reappear

A balloonist is directly above a straight road 1 9 miles long that joins two towns She finds that the town closer to her is at an angle of depression of 39 and the farther town is at an angle of depression of 32 How high above the ground is the balloon 399 1 9 mi Not to scale 320 The balloonist is about miles above the ground Round the final answer to two decimal places as needed Round all intermediate values to four decimal places

If x 28 what is m PQT In the figure above line TQ is tangent to a circle with center S at point Q and chord RQ is a diameter of the circle A 62 B 56 C 68 P D 118 R

Michelle is working on a design for a new building She has built a model of the building according to the client s specifications The height of the model is 15 inches the slant height of the model is approximately 17 inches and the base has a length of 14 inches and a width of 20 inches O A 5 600 cubic inches OB 280 cubic inches 980 cubic inches C W Michelle must order appropriate equipment to heat and cool the building so she must use the model to determine how much space there will be inside What is the volume of her model Round to the nearest hundredth if necessary Note picture not drawn to scale

A pole leans away from the sun at an angle of 6 to the vertical When the elevation of the sun is 54 the pole casts a shadow 43 ft long on level ground How long is the pole The pole is ft long Round to the nearest foot as needed

Find the angle of taper on the steel bar shown if it is equal to twice m The angle of taper of the steel bar is Round to the nearest minute as needed www 25 0 mm m 22 5 mm

73 3 points Given cos 2a and 2a is in quadrant I find exact values of the six trigonometric functions Note You are not allowed to use decimals in your answer sin a cos a tan a csc a sec a cot a

Consider circle C with radius 5 cm and a central angle measure of 60 C 60 5 cm S R What fraction of the whole circle is arc RS What is the approximate circumference of the circle cm What is the approximate length of arc RS cm

D A 110 C 36 B Use the drop down menus to complete the statements about the diagram The measure of AB is The measure of ZBOC is The measure of ADC is

Find the area of the parallelogram with vertices P1 P2 P3 and P4 P 7 5 5 P 4 4 8 P3 4 3 6 P4 15 2 9 O A O B 3074 2 3 70 2 OC 3 70 2074

The length of a rectangular garden is 3 times the width y The owner increases the width and length of the garden by 2 feet Which expression models the new area of the garden

function is defined for all real numbers as follows 10 x if 4 x 4 x 10 if x24 1 x Graph the function Then determine whether or not the function is continuous 12 10 13 10 6 8 10 V X

Figure F is graphed 1 Transform figure F using the rule x y x y 8 Sketch it on the graph 2 Describe the transformation precisely Translation along the directed line segment from point to point rotation direction and degrees reflection across line 3 Does the transformation result in a figure that is congruent to the original similar to the original both or neither T 10 9 4 2 10 8 6 4 2 0 ON 2 4 6 8 X 8 F 2 4 S 8 10

Line m is represented by the equation 3 y 2 x 4 Select all equations that rpresent lines perpendicular to line m Select all that apply y 3x 4 0y x 4 y x 4 y x 4 y 1 x 5 6 3 y 1 x 5 2

Which of the following points lies on the circumference of the circle x 3 y 12 29 sty 923 10 20 a 15 7 b 8 12 C 2 14 9 3 8 10 18

The circle is inscribed in triangle PRT P U 9 T S 5 R Which statements about the figure are true Select two options The perimeter of the triangle is 19 units TU TS PUTU The length of line segment PR is 13 units The length of line segment TR is 10 units

41 in The area isin 49 in Find the area

A D E B Chords AC and BD intersect at E with BD 7 units DI 2 units and AE 4 units What is the length of segment CE units

Find the area of the rhombus Note The dimensions shown are for half the diagonal 25 ft 22 ft

Of 50 students going on a class trip 35 are student athletes and 5 are left handed Of the student athletes 3 are left handed Which is the probability that one of the students on the trip is an athlete or is left handed Athletes 0 2 0 5 0 74 0 8 Left handed

15 tan X Z 40 50 Y 30 X

Find the surface area of the figure below 8 yd 17 yd 17 yd 17 yd 14 7 yd

Question 3 25 points Hamilton Circuits Paths Which of the below descriptions shows a possible HAMILTON PATH EFADECBA FECBAD ADEFBC ADECBAFE A D F E C B

4 The equation of the circle is x y 2x 6y 71 What are the coordinates of the center and the lengt of the radius of the circle 2 points a Radius 9 center 1 3 b Radius 9 center 1 3 c Radius 81 center 1 3 d Radius 81 center 1 3 O A O B O c C

By using C continuity combine two cubic B zier curve using 0 0 1 2 1 4 and 0 6 as control points for the first curve and 2 6 4 3 and 3 0 as the remaining control points of the second curve Calculate the first control points of the second curve

9 Write the term needed to create a perfect square trinomial m b p 6x a 81

4 5 9 CHAPTER 12 Find the volume of the figure Round your answer to two decimal places if needed 1 Quiz 2 18 cm 3 cm 14 in 12 ft 24 cm 4 cm 50 m 9 217 9 21 8 12 1005 3 8A V 6 0 12 2412 74 6 in 30 m 8 cm 4 cm

Find the volume of each of the following Round your tenth if necessary 3 a square prism with base length 7 m and height 15 m 4 a cylinder with radius 9 in and height 10 in 5 a triangular prism with height 14 ft and a right triangle base with legs measuring 9 ft and 12 ft 6 a cylinder with diameter 24 cm and height 5 cm

B C E D F ZFAE measures 72 What other angle must measure 72 OZBFD OZDEA O ZEDF OZFBE

The solids are similar Find the surface area of solid B Prism A 17 in S 346 in Prism B 34 in The surface area of solid B is square inches