Area Questions and Answers

Ive the word problem below 24 What is the perimeter of a rectangle that has vertices 2 5 2 6 and 6 6 Estimate an irrational answer to two decimal places

6 Find the volume of the solid that is formed by revolving the region bounded by 2 1 when 0 y 1 y r 1 when 1 r 0 and r 0 about the y axis using integration

Check that the four points P 2 4 4 Q 3 1 6 R 2 8 0 and S 9 2 1 all lie in a plane Then use vectors to find the area the quadrilateral they define Use symbolic notation and fractions where needed Enter DNE if the points do not lie in a plane

y 2x Video Example 1 2 EXAMPLE 1 Use rectangles to estimate the area under the parabola y 2x from 0 to 1 the parabolic region 5 illustrated to the left SOLUTION We first notice that the area must be somewhere between 0 and 2 because 5 is contained in a rectangle of side lengths 1 and 2 but we can certainly do better than that Suppose we divide the region into four strips by drawing vertical lines x as in the Figure a below and x y X No y 2x 2 Sy 4 Each rectangle has width and the heights are areas of these approximating rectangles we get 1 1 2 y 22 1 2 A 3 4 a We can approximate each strip by a rectangle whose base is the same as the strip and whose height is the same as the right edge of the strip as in Figure b above In other words the heights of these rectangles are the values of the and function f x 2x at the right endpoints of the subintervals 0 BI and 2 1 If we let R be the sum of the R 2 2 4 4 201 CO 1 b 15 8 x We see that the area A is less than R so A 15 8 x Instead of using the rectangles above we could use the smaller rectangles whose heights are the values off at the left endpoints of the sub intervals The leftmost rectangle has collapsed because its height is 0 The sum of the areas of these approximating rectangles is 1 2 4 1 2 0 1 2 1 2 7 x 4 We see that the area is larger than La so we have lower and upper estimates for A 718 X A 15 8 X We can repeat this procedure with a larger number of strips The figure shows what happens when we divide the S eight strips of equal width 7 8 1 1 x 11 2 a Using left endpoints b using right endpoiets By computing the sum of these areas of the smaller rectangles 4 and the sum of the areas of the larger rectangles Ra we obtain better lower and upper estimates for A

Suppose a Healthy Handwashing Survey is conducted and it was found that 56 of adult Americans operate the flusher of toilets in public restrooms with their foot Suppose a random sample of 19 adult Americans is obtained and the number who flush public toilets with their foot is recorded Is this a Binomial Experiment If yes what is n and what is p n P Use three decimal places for the following questions If 19 adult Americans is randomly selected find the probability that a Exactly 13 people flush public toilets with their foot b At most 12 people flush public toilets with their foot c At least 11 people flush public toilets with their foot d Between 10 and 15 including 10 and 15 people flush public toilets with their foot e In the space below explain how you found the answer to part c or part d You may choose which to ovplain Includo what you plugged culator to find the nowor

7 Two concentric circles are shown in the diagram The shaded region represents 36 of the total area of the outer circle that has the radius shown 58 cm O What is the radius of the inner circle to the nearest tenth of a centimeter

Determine the area of the hyperbolic triangles having the following angle measures if k 1800 i mLA 60 mLB 60 mLC 58 5 ii mLA 40 mLB 40 mLC 70 iii mLA 20 mLB 30 mLC 25

If the cones below are similar what is the ratio of the surface area of the larger cone to th surface area of the smaller cone 28 yd si Som 8 yd

The pyramids below are similar What is the ratio of the volume of the smaller pyramid to the volume of the larger pyramid SA 52 in type your answer SA 325 in type your answer

I need to paint a spherical storage tank in the pool It has a radius of 8 feet and the paint cans I bought will cover 75 square feet of the surface area How large is the surface area of the sphere 986sq feet 782sq feet 1082sq feet

The volume of a cube is 64 cubic centimeters What is the surface area of the cube 96cm 256cm 384cm 16cm

What is the circumference of a circle with a radius of 13in rounded to the nearest tenth 530 9 feet 81 7 feet 20 4 feet 530 feet

What is the circumference of a circle with a radius of 6ft in terms of T 127 ft 24 ft 6 ft 36T ft

Find the length of the arc O 12 6 km O 14 8 km O 42 2 km O 62 3 km 17 km 210

Find the length of the arc O 15 7 m O 14 8 m O 42 2 m O 18 4 m 20 m 45 None of the other answers are correct

Find the center and radius of the circle represented by the equation below x 11 y 11 64 Center 9

7 Find the area enclosed by three petals of the rose r 4 sin 50 10 points r usins 0

iangle must be 4 0 e find that m 42 0 mZ4 Property of Triangles ngle X

In the isosceles trapezoid below what is the measure of ZB A D 2x 27 B 5x 12 C

Given Quadrilateral ABCD with AB AC AB CD AB CD What best describes this shape Rhombus Rectangle Trapezoid Parallelogram

In parallelogram PQRS what is the value of Angle P S P 4y 7 10y 37 R O

ZJ and LM are base angles of isosceles trapezoid JKLM Ifm J 18x 8 and mZM 13x 13 f

In circle T the length of UV and m LUTV 110 Find the area shaded below 9 Express your answer as a fraction times T V T U

In circle L LM 5 and m ZMLN 144 Find the area of shaded sector Express your answer as a fraction times T N L M

In circle B with m ABC 74 and AB 12 units find area of sector ABC Round to the nearest hundredth C B A

Language a Volume of cylinders BM has a height of 11

de Volume of c cylinder has a hei 3 14 and ro

Trigonometry Spring 2023 Sp23 MATH 1106 90 TH 22 1 Points DETAILS Sketch the curve given by the parametric equations x 2t cost y 2t sin t 10 y 10 5 Homepa W Assignment 10 Parametric Equations t 0 5 10 X

5 The shaded area of a circle is 25 cm If the diameter of the circle is 10 cm determine what percentage c the circle is shaded

7 Find the diameter of a circle with an area of 74 mm2 Round your answer to the nearest tenth

The area of the shaded sector above is 97 and the length of OB 10 Determine what percentage of th circle is shaded in black A O 10 in B Jasiqanie u zimbet so gastodi diris 102 ai oborio slo 515

In circle H with m GHJ 46 and GH 4 units find area of sector GHJ Round to the nearest hundredth G J H

Find the Area of the composite figure below 7 8 00 10 b h 13

3 PREPARING FOR TOMORROW 18 36 18 in What is the radius of this circle 3A Using the circle to the left determine the are in terms of and to the nearest hundredths

Find f 30 6 mi miles 60 4 Write your answer in simplest radical form

OMICWOR Determine the volume and the surf

Write an equation for the function graphed be in factored form Use y as your output S 7 2 1 1 4

Determine a the area and b the perimeter of

Determine a the area and b the perimeter of the qu

14 Find the volume of the cone 3 000 mm 1 000 mm 300 mm 10 mm h 30 mm r 27

The area of a triangle may be found by using the formula 1 Area base x height 2 Find the area of the geometric figure 7 yd 12 yd

B si est Ato C Note Figure not drawn to scale length of arc BC is In the circle above point A is the center and the 2 3 3 3 5 circle What is the value of x of the circumference of the

For a project Carlos must provide one cut out paper model of each type of triangle acute right and obtuse He sketches each triangle on graph paper before making the models 10 Ix 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 89 X What is the total area of the three triangles 12 units 13units 13 units 14units

Michael is finding the area of parallelogram ABCD To do this he follows the steps in the table Step 1 Draw a rectangle around parallelogram ABCD Step 2 Find the area of the rectangle Step 3 Find the area of the four right triangles created in the corners of the rectangle Step 4 Subtract the area of the right triangles from the area of the rectangle To solve the problem using these steps what are the dimensions of the rectangle he should draw D 61 5 3 24 5 4 3 2 1 2 C A B 2 3 4 2 units by 4 units 3 units by 2 units 4 units by 4 units 5 units by 6 units X

Point P partitions the directed line segment from A to B into the ratio 3 4 Will P be closer to A or B Why A B P will be closer to A because it will be P will be closer to A because it will be P will be closer to B because it will be P will be closer to B because it will be the distance from A to B the distance from A to B the distance from B to A the distance from B to A

20 0 3 6 cm The actual length L of a rectangle is 30 centimeters Use the scale drawing of the rectangle to find the actual width W A 12 5 B 45 0 D 10 2 4 cm

B SSS A SSS D SAS B D By which reason can it be proven that ADAB and ADAC are congruent A AAS C

Insert a picture of your system model in the space below not a link to a picture This is NOT a copy and paste of the model below and is not just a re drawing of the same Draw a picture of the systems in your model interacting

From Lesson 8 09 Angle Measures of Po What is the value of x 4 140 100 degrees 120 degrees 130 degrees 34 X 56

What is the value of x 77 66 on 8 09 Angle Measures of P 6 8 59 62 12x