Tutors Answer Your Questions about Surface-area (FREE)
Question 1161779: An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort’s water rights effectively.
1. The resort owner wants to line the largest circular edge of the pool with 2 inches of 24K gold leaf. Explain how to determine how many linear feet of gold leaf you should plan to cover.
2. What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.
3. Inset in the floor of the restaurant is a circular fish tank with a diameter of 10 feet. The fish tank is concentric with the pool. Describe how to find the center point for that circle.
4. If the pool’s depth averages 4 feet, how much water will it take to fill the pool? (Hint: the volume of a cylinder is the area of the base times the depth.)
5. City ordinances only allow the resort to use 40,000 cubic feet of water in the pool without the fish tank. Show how to calculate the maximum depth the pool can be to stay under the 40,000-cubic-foot threshold.
6. How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet? Explain the difference in your calculations for questions 5 and 6. Does it change the maximum average depth of your water?
Click here to see answer by KMST(5385)   |
Question 1033020: A bucket full of water is in the form of a frustum of a cone. The bottom and top radii of the frustum are 18cm and 28cm respectively and the vertical depth is 30cm. If the water in the bucket is then poured into an empty cylindrical container with base radius 20cm, find the depth of the water in the container. (Take pie=22 over7
Click here to see answer by ikleyn(53906)  |
Question 448758: mrs lopez wants to tile your kitchen floor. her room is 10 ft by 12 ft. how many 1 foot square tile does she need to cover her floor.
i got that she will need 120 tiles since the area of the room is 120 i am not sure with this answer
pasrt b says that mrs lopez changes her mindand choosesz smaller tiles that are only 6 inches on each side. how many tiles does she need
Click here to see answer by josgarithmetic(39832) |
Question 448758: mrs lopez wants to tile your kitchen floor. her room is 10 ft by 12 ft. how many 1 foot square tile does she need to cover her floor.
i got that she will need 120 tiles since the area of the room is 120 i am not sure with this answer
pasrt b says that mrs lopez changes her mindand choosesz smaller tiles that are only 6 inches on each side. how many tiles does she need
Click here to see answer by ikleyn(53906) |
Question 731994: The 2  squares in the figure below have the same dimensions. The vertex of one square is at the center of the other square. What is the area of the shaded region, in square inches?
http://tinypic.com/r/1y678j/6 (the diagram)
Click here to see answer by ikleyn(53906) |
Question 1167256: If the area of a circle(A) has an area of a sector of the circle(a),an arc length(I) and circumference(C), deduce a formula for the arc length(I),in terms of the area of the sector and the radius of the circle(r). Hence calculate arc length of the sector of a circle with radius 5cm and area 25cm^2.
Click here to see answer by CPhill(2264)  |
Question 1210245: Evaluate the double integral by converting it into polar coordinates: integral from 1 to 2 integral from 0 to sqrt (2x - x^2) (x^2y + y^3) dy dx
I can get the answer using rectangular coords as 47/60, but conversion into polar and evaluation gets me the wrong answer. I can't seem to get the correct limits or whatever.
Click here to see answer by ikleyn(53906) |
Question 1210245: Evaluate the double integral by converting it into polar coordinates: integral from 1 to 2 integral from 0 to sqrt (2x - x^2) (x^2y + y^3) dy dx
I can get the answer using rectangular coords as 47/60, but conversion into polar and evaluation gets me the wrong answer. I can't seem to get the correct limits or whatever.
Click here to see answer by CPhill(2264) |
Question 1210280: A regular hexagon is below. Solve for the area of the hexagon.
https://ibb.co/dsnSzSLK
A watch has the SAME hexagonal face as the picture to the left. If the radius of the circle is 4, then what is the area between the hexagon and circle?
https://ibb.co/ynkmvtbs
Click here to see answer by ikleyn(53906) |
Question 1210165: If an isosceles trapezoid CDFG was added below,
where the height was the same as the triangle
above and the bases had a length of 12 and 24,
then what is the area of the new composite figure?
https://ibb.co/jZWQ628k
Click here to see answer by ikleyn(53906) |
Question 1210164: If an isosceles trapezoid CDFG was added below,
where the height was the same as the triangle
above and the bases had a length of 12 and 24,
then what is the area of the new composite igure?
https://ibb.co/jZWQ628k
Click here to see answer by ikleyn(53906) |
Question 1210167: A regular hexagon is below. Solve for the area of the hexagon.
https://ibb.co/dsnSzSLK
A watch has the SAME hexagonal face as the picture to the left. If the radius of the circle is 4, then what is the area between the hexagon and circle?
https://ibb.co/ynkmvtbs
Click here to see answer by ArschlochGeometrie(3) |
Question 1210167: A regular hexagon is below. Solve for the area of the hexagon.
https://ibb.co/dsnSzSLK
A watch has the SAME hexagonal face as the picture to the left. If the radius of the circle is 4, then what is the area between the hexagon and circle?
https://ibb.co/ynkmvtbs
Click here to see answer by mccravyedwin(421)  |
Question 1210163: Solve for the area of the composite figure.
https://ibb.co/cXV52NVm
If an isosceles trapezoid CDFG was added below, where the height was the same as the triangle above and the bases had a length of 12 and 24, then what is the area of the new composite figure?
https://ibb.co/jZWQ628k
Click here to see answer by mccravyedwin(421) |
Question 1210163: Solve for the area of the composite figure.
https://ibb.co/cXV52NVm
If an isosceles trapezoid CDFG was added below, where the height was the same as the triangle above and the bases had a length of 12 and 24, then what is the area of the new composite figure?
https://ibb.co/jZWQ628k
Click here to see answer by ArschlochGeometrie(3) |
Question 1210163: Solve for the area of the composite figure.
https://ibb.co/cXV52NVm
If an isosceles trapezoid CDFG was added below, where the height was the same as the triangle above and the bases had a length of 12 and 24, then what is the area of the new composite figure?
https://ibb.co/jZWQ628k
Click here to see answer by greenestamps(13362)  |
Question 1170042: Tank A and Tank B are rectangular prisms and are sitting on a flat table.
Tank A is 10 cm × 8 cm × 6 cm and is sitting on one of its 10 cm × 8 cm faces.
Tank B is 5 cm × 9 cm × 8 cm and is sitting on one of its 5 cm × 9 cm faces.
Initially, Tank A is full of water and Tank B is empty.
The water in Tank A drains out at a constant rate of 4 cm3/s.
Tank B fills with water at a constant rate of 4 cm3/s.
Tank A begins to drain at the same time that Tank B begins to fill.
(i) Determine after how many seconds Tank B will be exactly 1
3
full.
(ii) Determine the depth of the water left in Tank A at the instant when Tank
B is full.
(iii) At one instant, the depth of the water in Tank A is equal to the depth of
the water in Tank B. Determine this depth.
(b) Tank C is a rectangular prism that is 31 cm × 4 cm × 4 cm.
Tank C sits on the flat table on one of its 31 cm × 4 cm faces.
Tank D is in the shape of an inverted square-based pyramid, as shown. It is
supported so that its square base is parallel to the flat table and its fifth vertex
touches the flat table.
The height of Tank D is 10 cm and the side length of its square base is 20 cm.
Initially, Tank C is full of water and Tank D is empty.
Tank D begins filling with water at a rate of 1 cm3/s.
Two seconds after Tank D begins to fill, Tank C begins to drain at a rate of
2 cm3/s.
At one instant, the volume of water in Tank C is equal to the volume of water
in Tank D.
Determine the depth of the water in Tank D at that instant.
Click here to see answer by CPhill(2264) |
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