Area Questions and Answers

The radius of a sphere is measured as 9 centimeters with a possible error of 0 025 centimeter a Use differentials to approximate the possible propagated error in cm in computing the volume of the sphere error t cm3 b Use differentials to approximate the possible propagated error in cm in computing the surface area of the sphere cm error t c Approximate the percent errors in parts a and b Round your answers to two decimal places volume surface area

Find the surface area of the composite figure 3 cm 5 cm 4 cm 8 cm 8 cm 5 cm 7 cm 10 cm SA cm Enter

10 ft 8 ft 6 ft Find the area of this figure Round your answer to the nearest hundredth Use 3 14 to approximate A ft Notice that only half of the circle is included in the figure Enter

The length of a picture frame is 7 inches more than the width For what values of x is the perimeter of the picture frame greater than 154 inches loca For X the perimeter of the picture frame is greater than 154 inches Type an integer or a decimal X X

You are building a patio of the back of your house The diagram shows the plan for the patio Each unit in the coordinate plane represents 1 5 feet Find the area of the patio to the nearest square foot TY 10 8 6 A B OC D 2 about 57 ft 2 about 39 ft 2 about 38 ft 2 about 26 ft 2 4 house 6 8

ose a table to fit in a very small space He has 5 choices and wants to choose the table with the smallest area Which of the table tops below has the smallest area Select the correct answer below O O 2 3 2 3 4 3

A garden is shaped like a regular hexagon Each side of the hexagon measures 10 meters and the heigh of one of the isosceles triangles in the hexagon is about 9 meters Using these dimensions what is the area of the hexagon The area of the hexagon is m

Kevin s grandmother gave him an old lamp that needs a new lampshade He wants to buy some fabric to make a new lampshade The lampshade is 10 inches tall The diameter of the top is 6 inches The diameter of the bottom is 10 inches The formula for finding the lateral area of the shade is A 2 where is the radius of the top 2 is the radius of the bottom and h is the height of the lampshade deel is mss 6 efnow e Select the area that is the best approximation for the amount of fabric he needs to buy 541 4 square inches 474 1 square inches 321 8 square inches is mas of

Find the surface area of the composite figure 4 cm 3 cm 4 cm 13 cm SA 12 cm 2 cm 5 cm 3 cm Enter

Which of the following integrals represents the area enclosed by the smaller loop of the graph of r 1 2 sin B E 11 6 7 6 11 6 7 6 6 6 7 6 1 2 sin 0 de 1 2 sin 8 de 1 2 sin 0 de 1 2 sin 0 de 6 1 2 7T 6 1 2 sin e de

Question 2 W B Q 0 1 25b D B 0 b C 0 0 A a 0 A plan for a triangular garden was plotted on coordinate axes with vertices A a 0 B 0 b and C 0 0 as shown The plan was then modified to enlarge the garden to include the shaded region as represented in the diagram Which of the following best describes the relationship between the area of the enlarged garden and the area of the original garden The total area of the enlarged garden would be 1 25 times the area of the original garden because the original garden s dimensions are scaled by 1 25 to create the dimensions of the enlarged garden P 1 25a 0 The total area of the enlarged garden would be 1 0 25 0 25 times the area of the original garden because both the length and width of the garden were increased by 0 25 units The total area of the enlarged garden would be 1 252 times the area of the original garden because the original garden s dimensions are scaled by 1 25 to create the dimensions of the enlarged garden The total area of the enlarged garden would be 1 0 25 1 0 25 times the area of the original garden because both the length and width of the garden were increased by 0 25 units

Raymond has a circular garden with a radius of 9 feet He wants to build a walkway that is feet wide around the garden A What will the area of the walkway be in square feet B C D 16T 25T 4 ft 81T 9 ft

In Exercises 21 and 22 the area of the shaded sector is shown Find the indicated measure See Example 4 21 area of OM K 50 M 22 radius of OM L M 89 K A 56 87 cm A 12 36 m AS marr 360

The diameter of a standard basketball is 9.5 inches. If the basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four basketballs?

Four congruent isosceles right triangles are added to the edges of a regular octagon to form a square, as shown. If the legs of each of the four triangles are 3 centimeters long, which measure is closest to the perimeter of the octagon? OA. 24.0 cm OB. 25.5 cm OC. 33.9 cm OD. 72.0 cm

The Walmart parking lot is a rectangle that measures 420 feet long and 218 feet wide. Each parking space is a rectangle that measures 18 feet long and 9 feet wide. The Saturday before school starts, the parking lot is full. How many cars are parked in the parking lot at Walmart on the Saturday before school starts? Hint: Calculate the area of the parking lot and the area of a parking space to help find the answer. 430 cars 565 cars 670 cars 775 cars

If two opposite sides of a square are increased by 7 meters and the other sides are decreased by 2 meters, the area of the rectangle that is formed is 36 square meters. Find the area of the original square. Must use a quadratic equation to solve the problem for any credit.

The diagram below shows two spheres, one with diameter 12 cm and one with diameter 9 cm. What is the difference in their surface areas?

Let R be the area bounded by the graph of y = 16-x² and the x-axis over [0,2]. a) Find the volume of the solid of revolution generated by rotating R around the x-axis. b) Find the volume of the solid of revolution generated by rotating R around the y-axis. c) Explain why the solids in parts (a) and (b) do not have the same volume.

Approximate the area under the graph of f(x) = 0.05x - 1.44x² +56 over the interval [2,6] by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval. The area under the graph of f(x) = 0.05x - 1.44x² +56 over the interval [2,6] is approximately.

Which of the following describes the area of the region in quadrant II bounded by f(x), g(x), and the y-axis, if f(x) = x2 - 2x and g(x) = -3x - x² + 3?

For the regions A and B shown in the graph: Part A: Discuss the limits of integration. (3 points) Part B: Set up an integral expression that represents the total area. (4 points) Part C: Calculate the total area. (3 points)

You have 1260 feet of fencing to enclose a rectangular garden. What are the length and width of the garden which will maximize the area? Write your two dimensions separated by a comma. For example, if the garden should be 20 feet long by 10 feet wide, write 20,10.

A circle has a diameter of 20 units. Find the area 100π 10π 20π 400π

A pen stand made of wood is in the shape of a cubold with four conical depressions to hold pens. The dimensions of the cubold are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand. Use it = 22/7. 529.68 cm³ 520.48 cm³ 523.53 cm³

Find the volume of the rectangular pyramid whose base is 3 m x 6 m and whose height is 5 m. 60 m³ 90 m³ 30 m³

Find the area of an obtuse triangle with a base of 8 inches and a height of 5 inches. A. 40 square inches B. 20 square inches C. 45 square inches

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter and the diameter of the spherical part is 8.5 cm. Find the volume of the flask. Use π= 3.14 355.76 cm³ 350.25 cm³ 346.51 cm³

A general contractor is constructing a building that requires a concrete foundation that is to be 15 feet by 18 feet and 18 inches thick. If the local home supply store sells concrete for $75 per cubic yard, what will be the cost of the concrete for the foundation? Express your answer rounded up to the next whole dollar.

Find the area of the triangle. a=14, b=17, c = 22

The dimensions of a triangular lot are 198 feet by 188 feet by 197 feet. If the price of such land is $3 per square foot, how much does the lot cost? The lot costs $ __ (Do not round until the final answer. Then round to the nearest cent as needed.)

Fill in the blank. The graphs of the tangent, cotangent, secant, and cosecant functions all have -Select--- asymptotes. horizontal vertical slant

Find the area and perimeter of the figure below. Do not forget units. Arc AB is a semicircle (half of a circle, ABC is a right triangle, AB = 16 yards, BC = 12 yards and AC = 20 yards. Area = Perimeter =

A certain forest covers an area of 2500 km². Suppose that each year this area decreases by 3.5%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.

You have 80 yards of fencing to enclose a rectangular region. a) Write a function for the area of the rectangular region in terms of x. b) Find the dimensions of the rectangle that maximize the enclosed area. c) What is the maximum area?

Which formulas can be used to find the surface area of a right prism where p is the perimeter of the base, h is the height of the prism, BA is the area of bases, and LA is the lateral area? Check all that apply. A. SA = BA + ph B. SA = BA+ 1/2 LA C. SA = BA + 1/2 ph D. SA = BA + LA E. SA - BA - LA

The four sequential sides of a quadrilateral have lengths a = 5.3, b = 7.2, c = 9.7, and d = 10.9 (all measured in yards). The angle between the two smallest sides is a = 116°. What is the area of this figure? area = yd²

The ratio of the lengths of the corresponding sides of two rectangles is 8:3. The area of the larger rectangle is 320 ft2. What is the area of the smaller rectangle? 120 ft² 90 ft² 30 ft² 45 ft²

A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in². Use the formula A = 4r, to find the radius of the beach ball. A represents the surface area r represents the radius of the sphere a. 24 in b. ±24 in c. 288 in d. 576 in

If the diameter of a sphere is 4 ft, then what is its surface area? Leave your answers in terms of π A. 14π m² B. 16 m² C. 2π m² D.16π m²

Find the area of a triangle with legs that are: 9 mm, 6 mm, and 12 mm. A. 12.3 mm² B. 11.6 mm² C. 37 mm² D. 26.1 mm²

If the coordinates of a parallelogram are Q(3, -2), R(7, -2), S(9,3), and T(5,3), the area of the parallelogram is: A. 30 units² B. 10 units² C. 20 units² D. 40 units²

What is the number of square units in the area of the triangle whose vertices are points A(2,0), B(6,0), and C(8,5)? A. 30 units² B. 6 units² C. 15 units² D. 10 units²

A circle has a diameter of 20 cm. What is the area of a sector bounded by a 208° arc? Use the key on your calculator to approximate . Round your answer to the nearest tenth.

What is the surface area of a cube with an edge length of 15 cm? 225 cm² 30 cm² 1350 cm² 3375 cm² None of the other answers

Suppose the dimensions of your dining room are 12 feet by 14 feet. You purchase a rectangular table that is 7 feet by 9 feet. After you put the table in the dining room, how much space is left in the dining room (in square feet)?

Find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches. Enter your answer to the nearest tenth.

The average distance from the planet Venus to the Sun is 6.7 x 10 mi. What is the area of the planar region swept by the line segment from the center of Venus to the center of the sun in one orbit around the sun? Assume a circular orbit. (Area Epts of circle: A=m², circumference of a circle: C= 2)

Use geometric formulas to find the unsigned area between the graph of y=f(x) and the x-axis over the indicated interval. f(x)=x+10; [-1,11] The area between f(x) and the x-axis is.____ (Type an exact answer, using as needed.)

A blueprint of a house shows a bedroom with an area of 12 square inches. If the blueprint's scale is 1 inch : 3 feet, what would be the actual square footage of the bedroom? square feet