Area Questions and Answers

What is the surface area of fish tank in the shape of a cube that has volume of 90 cubic inches? 90 square inches 45 square inches 30 square inches 120 square inches

Find the area of the sector of a circle with radius 6 miles formed by a central angle of 205°: square miles Round your answer to two decimal places.

Find the area bounded by the given curves. y = 8x³ + 9 and y = 8x + 9

Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your result. (Round your answer to three decimal places.) y = x² + 4 / x , x = 1, x = 2, y = 0

Using the trapezoidal rule and 4 even intervals, find an approximation for the area under the curve of f(x) = 2/x in the interval [2, 7]. Give your answer correct to 2 decimal places without specifying units.

Find an approximation for the area under the curve of f(t) = -2 + 4t in the interval [1,3.8] by using the trapezoidal rule. Divide the interval into sub-intervals of length 0.7 and give your answer correct to 3 significant figures without specifying units.

Sketch a cylinder with radius 5 feet and height 7 feet, then find the volume.

Problem Number One: What kind of data would I get if I asked everyone in the class. A) how many coins are in a sealed jar? B) weigh the next cat they can weigh after going home...? C) what they know of the Mu variant? D) to count the number of cans of soup at their local grocery store?

The scale in the drawing is 3 cm:5 m. Drag and drop the correct numbers into the boxes to give the length, width, and area of the actual room.

Fencing a Rectangular Corral Consider a rectangular corral with two partitions, as in Fig. 15. Assign letters to the outside di- mensions of the corral. Write an equation ex- pressing the fact that the corral has a total area of 2500 square feet. Write an expression for the amount of fencing needed to construct the corral (including both partitions).

Dracula purchased a box of cookies for his Halloween party. The box is in the shape of a triangular prism (see diagram). If the volume of the box is 3,240 cubic centimeters, what is the height of the triangular face of the box? How much packaging material was used to construct the cracker box? Explain how you got your answer. Solve using the THINK

Given the function f(x) = 10 log(x + 3), find the area of the region bound by the graph of y = f(x), the x-axis, and the line x = 4. Give your answer rounded to three significant figures. 76.2 63.3 33.1 27.5

A sphereing ball contains a sphere within a sphere. The diameter of the inner sphere is 2.1 meters. The outer sphere of the sphereing ball has a diameter of 2.8 meters. Find the volume within the outer sphere but outside the inner sphere. (Round your answer to two decimal places.)

Wayne is hanging a string of lights 67 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is 7 feet longer than twice its width. Find the length and width of the patio.

The rectangle below has an area of 55x6 +22x4. The width of the rectangle is equal to the greatest common monomial factor of 55% and 22x¹. What is the length and width of the rectangle?

The length of a rectangle is 4 inches longer than it is wide. If the area is 140 square inches, what are the mdimensions of the rectangle? The width, or shorter side is The length, or longer side is

A rectangle has sides that measure 11x + 1 units long and 6x + 5 units long. What are the expression that represent the perimeter and area of the rectangle?

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular let area of triangles ABC,ACD and ADB be 8, 9 and 6 square units respectively. find the area of triangle BCD.

You want to put a 5 inch thick layer of topsoil for a new 33 ft by 12 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards. cubic yards

Sheet metal is used to make a vent transition piece that is in the shape of a frustum of a pyramid with one square opening of 12 in and the other square opening of 9 in. The slant height is 15 in. What is the perimeter of the 12 in opening? P₁= What is the perimeter of the 9 in opening? P2= How many square inches of sheet metal needs to be used to create the transition piece? L = in Using 1 sq ft = 144 sq in, how many square feet of sheet metal are needed (do not round)? The transition piece requires_________sq ft of sheet metal.

A metal silo is made by two basic shapes: a cylinder and a hemisphere. The cylinder part of the silo is 50' high and the radius of the silo is 16. Using = 3.14, what is the circumference of the cylindrical part of the silo? C = What is the lateral surface area of the cylindrical part of the surface area? L = A/ ft Using π = 3.14, what is the surface area of the hemisphere top? S= A sq ft Assuming the base is made of concrete, how many total square feet are needed to make the silo? A sq ft of sheet metal.

Type your answer and then click Done. The radius of the base of a cone is 22 m. Its slant height is 10 m. Find the surface area in terms of .

The base of a prism has a perimeter of 12 centimeters and a height of 2 centimeters. The area of its base is 5 square centimeters. What is the surface area of the prism? F 23 cm² G 34 cm² H 50.5 cm² J 60 cm²

A cylinder-shaped piece of lead has a radius of 4 cm and a height of 13 cm. If the lead piece weighs 19,521 grams, how much does one cubic centimeter of the object weigh in grams? . Write your answer as a number only. No unit. Round your answer to one decimal place if necessary. .

A rectangle has an area of 874 square inches. Its width is eight inches less than twice the length. Find the measures of the length and width of the rectangle. The length measures The width measures

To completely cover a spherical ball, a ball company uses a total area of 36 square inches of material. What is the maximum volume the ball can have? Note: the surface area of a sphere is 4r² and the volume of sphere is 4/ 3 πr3

6 The sides of a rhombus have length 16 cm. The longer diagonal has length 22 cm. Find the area of the rhombus. . Write your answer as a number only. . Round answer to the nearest tenth (one decimal place) if needed.

If the side lengths of a cube are dilated from 2 yards to 29 yards, find the scale factor that relates the area of one face of the original cube to a face of the scaled cube. . B Write your answer as a number only. Round your answer to two decimal places if necessary.

Approximate the area under the curve y = x² from a = 2 to x = 4 using a Right Endpoint approximation with 4 subdivisions.

Courtney is building a rectangular wading pool. She wants the area of the bottom to be 54 square feet. She also wants the length of the pool to be 3 ft longer than twice its width. What is the length of the pool in feet? 6 3 27 9 18

3. Jackson's rectangular bedroom has an area of 90 square feet. The area of his bedroom is 9 times that of his rectangular closet. If the closet is 2 feet wide, what is its length? how muoy woria.o1 abyow TO srit biv/263mb 2 bos gnol es zomi 2 zi muhoji deriW Jest Al to istamineq s riw gnol jest A al vis dil nottasjong lugnt

The side of a square is measured and found to be 6.78 inches long with a possible error of 0.03 inches. Use a differential to estimate the possible error that might result when computing the area of the square.

You have three pleasure horses in a rectangular pasture 550 feet wide and 800 feet long. The pasture has a five-board-high fence along the width in front (550 feet). The remainder of the fence is constructed of woven wire with a board on top. Woven wire is sold in 20 rod rolls. (Note: 1 rod = 16.5 feet) a. How many acres are in the pasture? b. How many linear feet of boards were used? c. How many rolls of wire were purchased? Saver

A 1.5-mm layer of paint is applied to one side of the spherical zone generated when the upper portion of the circle x² + y2 = 81 on the interval [-5, 5]) is revolved about the x-axis. Find the volume of paint needed assuming that x and y are measured in meters.

MODELING WITH MATHEMATICS The area (in square centimeters) of a square coaster can be represented by d2 + 8d + 16. a. Write an expression that represents the side length of the coaster. and Fa b. Write an expression for the perimeter of the coaster.

David has 200 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) =

David has 80 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) =

An abandoned lot is to be converted into a community garden. The garden is to consist of a 7 yard by 20 yard rectangle for planting that is surrounded by a path of uniform width. The total area of the lot is 198 square yards. What is the width of the path?

Consider the graphs of y = -1/2 x and y = 2|x|-a, where a € Z². a) Sketch the graphs on the same set of axes. b) Given that the graphs enclose a region of area 40 square units, find the value of a.

The length of a rectangle is 2 yd longer than its width. If the perimeter of the rectangle is 40 yd, find its area.

Find the length of the rectangle with an area of 575m² and a width of 25 m.

The volume of a rectangular prism box can be represented by the function V(x) = 2x3-5x2-3x. If the height of the box is x cm, which of the following can represent the length and width of the container? 1 and x + 3 2x + 1 and x-3 02x-1 and x + 3 02x-1 and x-3

A cylinder-shaped log 78 in. long measures 37.68 in. around. What is the volume of the log? Enter your answer as a decimal in the box. Use 3.14 for TT. in³

A square of an unknown side length x inches has one side length increased by 4 inches and the other increased by 7 inches. (a) If the original square is shown below with side lengths marked as x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above. (b) Label each portion of the second diagram with their areas in terms of x (when applicable). State the product of (x+4) and (x+7) as a trinomial below. (c) If the original square had a side length of x=2 inches, then what is the area of the second rectangle? Show how you arrived at your answer. (d) Verify that the trinomial you found in part (b) has the same value as (c) for x = 2.

Diana has 2400 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part. A. 29 sq. cm. B. 33 sq. cm. C. 31 sq. cm. D. 35 sq. cm.

Select the correct answer. A waffle is rolled to make a cone shape without any gaps or overlaps. The radius of its base is 2.5 centimeters, and its slant height is 11.5 centimeters. The company wants to save money on the cone by reducing the size. Which change would result in the biggest reduction of the lateral surface area of the cone? A.decrease radius by 0.2 cm and slant height by 0.3 cm B.decrease slant height by 0.5 cm C.decrease radius by 0.5 cm D.decrease radius by 0.3 cm and slant height by 0.2 cm

Jake cuts out a rectangular piece of paper that measures 5 x 4 inches. Andrea cuts out a paper sector of a circle with radius 15 inches and arc length of 3r inches. Whose paper is larger? SHOW YOUR WORK TO EXPLAIN YOUR ANSWER.

A microscope allows a scientist to see a circular region that is 1.29 millimeters in diameter. How much area, to the nearest square centimeter, can the scientist see? The area of the circular region is approximately. cm². (Do not round until the final answer. Then round to the nearest thousandth as needed.)

If, for all real numbers x, f(x) = g(x) + 3, then on any interval [a, b] the area of the region between graphs f and g is 3a-3b 3ab 3a + 3b 3b-3a