Questions on Geometry: Area and Surface Area answered by real tutors!

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Question 1137734: a swimming pool is 50m long. the water is 1 metre deep at the shallow end and 3m deep at the deep end. if the bath is 10 m wide, find the volume of water in the pool.
Click here to see answer by josgarithmetic(39617)

Question 1137934: A block of metal is cast into a solid cylinder whose volume is 10cm^3. Show that the cylinder has a minimum surface area when r= 3 root (5 over pi). The ends are included.
Click here to see answer by greenestamps(13200)

Question 1137932: A cylindrical metal container, open at the top, is to have a capacity of 24 cubic metres. The cost of material used for the bottom of the container is $0.15 per square metre, and the cost of the material used for the curved part is $0.05 per square metre. Find the dimensions that will minimise the cost of the material, and hence show the minimum cost is $2.64.
Click here to see answer by greenestamps(13200)

Question 1138098: Topic is Area, Circumference, and Perimeter
A park is 300 yds by 500 yds. There is a 4 wide foot walking path going around the entire perimeter of the park. The rest of the park is green space. How much green space is there in the park?

Click here to see answer by ikleyn(52781)

Question 1138218: A cube has a surface area of 126 ft.². What is the area of one face?
Click here to see answer by josgarithmetic(39617)

Question 1138494: The diagram below shows a square whose side is 1 and also two arcs with centres at points A and D. What is the area of the shaded surface?
Diagram link: http://i66.tinypic.com/2rr6ngp.jpg
Click here to see answer by MathLover1(20849)

Question 1138591: If a penny has a circumference of 59.69 millimeters, what is the radius of a penny?

Click here to see answer by ikleyn(52781)

Question 1138671: The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
Click here to see answer by Edwin McCravy(20055)

Question 1138671: The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
Click here to see answer by Alan3354(69443)

Question 1138672: Painting a Bedroom
The walls and ceiling inside your bedroom need to be painted. To save money, you decide that you will paint the bedroom yourself. Use the following information to solve this problem:
• The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
• The inside of the bedroom door will be painted the same color as the walls.
• Two coats of paint will be applied to all of the painted surfaces.
• The room has one window, measuring 3 feet, 9 inches by 4 feet, which will not be painted.

Click here to see answer by josgarithmetic(39617)

Question 1138674: Painting a Bedroom
The walls and ceiling inside your bedroom need to be painted. To save money, you decide that you will paint the bedroom yourself. Use the following information to solve this problem:
• The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
• The inside of the bedroom door will be painted the same color as the walls.
• Two coats of paint will be applied to all of the painted surfaces.
• The room has one window, measuring 3 feet, 9 inches by 4 feet, which will not be painted.
Discuss different ways to construct the room that will be painted. Are there any restrictions on where the window and door will be located? Will the overall amount of paint that is needed change based on where these are placed in the room?

Click here to see answer by josgarithmetic(39617)

Question 1138770: A company makes steel rods shaped like cylinders. Each rod has a radius of 2 centimeters and a height of 60 centimeters. If the company used 54,259.2 cm3 of steel, how many rods did it make?
Click here to see answer by ikleyn(52781)

Question 1139006: A hemisphere of diameter 10cm is attached to a cylinder of equal diameter. If the total length of the shape is 20cm calculate:
A) the surface area of the hemisphere
B)length of cylinder
C) surface area of the whole shape
Click here to see answer by greenestamps(13200)

Question 1139171: The surface area of a closed cone of height h and base radius r is given by
A = πr² + πr√(h² + r²).
Show that h = (A/πr)√(1 - (2πr²/A))
Click here to see answer by josgarithmetic(39617)

Question 1139171: The surface area of a closed cone of height h and base radius r is given by
A = πr² + πr√(h² + r²).
Show that h = (A/πr)√(1 - (2πr²/A))
Click here to see answer by MathLover1(20849)

Question 1139717: If the height, length, and width of a rectangular prism are decreased by 1/3, then the surface area would decrease by what ratio?
Click here to see answer by josgarithmetic(39617)

Question 1139791: The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the area of these two spheres?
Click here to see answer by Alan3354(69443)

Question 1139791: The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the area of these two spheres?
Click here to see answer by greenestamps(13200)

Question 1139809: A company makes two similar cylindrical containers. The total surface area off the smaller container is 0.64 times that of the larger container. The height of the larger container is 200cm. What is the height of the smaller container?
Click here to see answer by ikleyn(52781)

Question 1139855: The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?
Click here to see answer by josgarithmetic(39617)

Question 1139904: The volumes of two spheres are in a ratio of 8:216. What is the ratio of their areas?
Click here to see answer by Alan3354(69443)

Question 1140215: Where did the 3 come from in this problem?
The greenhouse behind your house is 42 feet long by 24 feet wide.
What is the distance around the greenhouse in yards
2*42+2*24=132/3=44 yds

Click here to see answer by josgarithmetic(39617)

Question 1140720: The area of a rectangle is 48cm^2 ,the length is halved and the width is tripled. What is the new area in cm^2
Click here to see answer by ankor@dixie-net.com(22740)

Question 1140778: The volume of a sphere is 5,000 pi m^3, What is the surface area of the sphere to the nearest square meter.
Click here to see answer by josgarithmetic(39617)

Question 1140788: Investigate different types of paint for painting outside a house show a table of different paints available and the price per litre

Click here to see answer by ikleyn(52781)

Question 1141125: An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

Click here to see answer by josgarithmetic(39617)

Question 1141329: Two cylinders of equal radii have heights in the ratio of 1:3. If the total surface area of the two cylinders is 770cm2 and the shorter cylinder is 7 cm high, find the common radii?

Click here to see answer by greenestamps(13200)

Question 1141391: A company makes steel rods shaped like cylinders. Each rod has a diameter of
4 centimeters and a height of 90 centimeters. If the company used 30,520.8 centimeters cube of steel, how many rods did it make?

Click here to see answer by math_helper(2461)

Question 1141521: In 2014 The Lindt Chocolate Company released a Christmas Special‐ the “Lindt Chocolate Maxi‐ Ball”. It was a Spherical container of diameter 20cm that resembled a Lindt Chocolate. Inside were a number of Lindt chocolate truffles. The weight of the maxi ball was 550g.
a. Calculate the volume of the Lindt Chocolate Maxi Ball (remember the diameter is above)
b. If the diameter of the smaller individual truffles is 2.5cm, how many could possible fit into the Max Ball‐ the extra packaging of the lindt chocolate (the clear ruffles ties) is negligible and will not be factored into the calculations.
c. Using your answer in b. calculate the approximate weight of each individual Lindt Chocolate Truffle
Click here to see answer by ikleyn(52781)

Question 1141583: The length of a rectangle is 5 inches longer than twice the width, and the area is 12 inches squared. Let l represent the length and w represent the width. Which of the following equations correctly models the situation?

Click here to see answer by ikleyn(52781)

Question 1141639: Find the area of the isosceles trapezoid.
a. 54 m2
b. 72 m2
c. 324 m2
d. 162 m2
Copy and paste link to see photo. Thank you!
file:///var/folders/qj/n0cgwdpn5277fjjwqrp380300000gn/T/com.apple.Safari/WebKitDropDestination-KQXOpLX3/Screen%20Shot%202019-05-29%20at%205.15.54%20PM.png

Click here to see answer by josgarithmetic(39617)

Question 1141681: The length of a rectangular room is 9 less than twice the width, and the width is 18feet. If square porcelain tiles 3 feet long are used to cover the floor, how many tiles are needed?
A)27
B)54
C)81
D)162
Click here to see answer by josgarithmetic(39617)

Question 1141705: From a point on the ground 160 metres from the base of a building, an observer finds that the angle of elevation to the top of the building is 39 degrees and that the angle of elevation to a pole atop the building is 41 degrees. What is the height of the building and the length of the pole in metres to two decimal places?
Click here to see answer by ikleyn(52781)

Question 1141706: Find the surface area of a cylinder with radius 10 cm and height 13 cm.
a. 1632.8 cm^2
b. 1583.4 cm^2
c. 722.2 cm^2
d. 1444.4 cm^2
Click here to see answer by ikleyn(52781)

Question 1141708: Find the similarity ratio of two circles with areas 75cm^2 and 27cm^2.
a. 25:9
b. 225:81
c. 75:27
d. 5:3
Click here to see answer by ikleyn(52781)

Question 1141733: Find the lateral area of a cylinder with height 4 ft and radius 4 ft.

a. 16ft^2
b. 32 ft^2
c.16(pi sign) ft^2
d. 32 (pi sign)ft^2

Click here to see answer by greenestamps(13200)

Question 1141735: A pizza with a 10-inch diameter is cut into 8 pieces. Find the area of one piece of pizza.

3.9 in^2
39.3 in^2
9.8 in^2
21.7 in^2
Click here to see answer by Boreal(15235)

Question 1141735: A pizza with a 10-inch diameter is cut into 8 pieces. Find the area of one piece of pizza.

3.9 in^2
39.3 in^2
9.8 in^2
21.7 in^2
Click here to see answer by ikleyn(52781)

Question 1141736: Find the lateral area of a regular square pyramid with base edge 6 cm and lateral edge 5 cm.
84 cm^2
96 cm^2
12 cm^2
48 cm^2
Click here to see answer by ikleyn(52781)

Question 1141740: The area formula for a regular polygon is 1/2 ap. What is the area of a regular pentagon with side length of 30 cm and apothem 5 cm?
450 cm^2
375 cm^2
750 cm^2
Click here to see answer by ikleyn(52781)

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