Solid Geometry Flashcards
Set 1 Problem 6: A bucket in the form of a frustum of a cone has a top diameter 25 cm and bottom diameter 15 cm. The perpendicular distance between the top and bottom is 28 cm. Find the total area of the material needed to make the bucket if it is open at the top.
1,964 cm² (p. 8)
Set 1 Problem 9: A water container has a square base 2 ft by 2 ft. A metal sphere is placed fully submerged inside the container causing water to rise 0.16 ft. What is the radius of the metal sphere?
0.53 ft (p.8)
Set 1 Problem 16: A hollow metal pipe is 30 cm long. The cross-section has an inner diameter of 2.5 cm and outer diameter of 3.2 cm. Find the volume of metal needed to make the pipe.
94 cm³ (p. 9)
Set 1 Problem 22: A right pyramid has a hexagon base with sides 12 cm each. The lateral edge of the pyramid measures 28 cm. Find the lateral area of the pyramid.
984.60 cm² (p.10)
Set 1 Problem 31: A spherical buoy 1.2 m in diameter sinks to depth of 0.80 m in a certain liquid. What is the ratio of the volumes of the spherical segment above the liquid to the total volume of the sphere?
0.26 (p.12)
Set 1 Problem 38: A firm producing poultry feeds finds that new production method needs to purchase an equipment costing P36,000 and the cost of each feed is P792 and the management plans to charge P1,260 per unit for the feed. Determine the revenue function R(x) from the sales of x feeds.
1,260x
Set 1 Problem 45: A frustum of a sphere has diameters of the bases 10.8 cm and 24.4 cm. The thickness of the frustum is 6 cm. Find the radius of the sphere.
14.05 cm (p.13)
Set 1 Problem 53: The first quadrant area bounded by y²=8x and x=2 is revolved about the x-axis. Find the volume of the paraboloid generated.
16π (p.14)
Set 1 Problem 64: An open-topped rectangular box is to have a square cross-section and has a capacity of 12,000 cm³. Find the height of the box that requires the minimum amount of material in making it.
14.42 cm (p.16)
Set 2 Problem 3: The area of a cross-section of a right circular cone is 20, and the area of the base is 45. If the altitude of the cone is 6, how far from the base is the cross-section?
(p. 23)
Set 2 Problem 4: Find the altitude of the right prism for which the area of the lateral surface is 143, and the perimeter of the base is 11.
13
Set 2 Problem 19: Find the angle of the sector that should be removed from a circular piece of canvas of radius 12 ft so that the conical tent made from the remaining piece will have a height of 7 ft.
67.60 degrees (p. 25)
Set 2 Problem 52: A frustum of a sphere has diameters of the bases 10.8 cm and 24.4 cm. The thickness of the frustum is 6 cm. Find the volume of the frustum.
1791 cm^3
Set 3 Problem 16: A frustum of a sphere has diameters of the bases 10.8 cm and 24.4 cm. The thickness of the frustum is 6 cm. Find the area of the zone of the frustum.
530 cm^2 (p.43)
Set 4 Problem 4: The volume of water in hemispherical tank is 1,470,265cm^3. If the depth of water in the tank is 6cm, find the radius of the tank in cm.
15cm (p.60)
Find the capacity of the following tanks whose shape and dimensions are given:
Set 4 Problem 29: A tank with rectangular top 10 ft by 4 ft, a rectangular bottom 10 ft by 2 ft, and a depth of 3 ft. The ends of the tank are equal trapezoids.
90 ft^3 (p. 64)