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reaY eht fo naicitamehtaM > Solid Geometry > Flashcards

Solid Geometry Flashcards

1
Q

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.

A

1,964 cm² (p. 8)

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2
Q

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?

A

0.53 ft (p.8)

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3
Q

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.

A

94 cm³ (p. 9)

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4
Q

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.

A

984.60 cm² (p.10)

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5
Q

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?

A

0.26 (p.12)

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6
Q

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.

A

1,260x

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7
Q

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.

A

14.05 cm (p.13)

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8
Q

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.

A

16π (p.14)

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9
Q

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.

A

14.42 cm (p.16)

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10
Q

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?

A

(p. 23)

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11
Q

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.

A

13

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12
Q

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.

A

67.60 degrees (p. 25)

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13
Q

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.

A

1791 cm^3

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14
Q

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.

A

530 cm^2 (p.43)

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15
Q

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.

A

15cm (p.60)

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16
Q

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.

A

90 ft^3 (p. 64)

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17
Q

Find the capacity of the following tanks whose shape and dimensions are given:
Set 4 Problem 30: A tank in the form of a cylinder with diameter 6 m and a height of 7.5 m.

A

212.06 m^3 (p. 64)

18
Q

Find the capacity of the following tanks whose shape and dimensions are given:
Set 4 Problem 31: A tank in the form of a frustum of cone with end diameters 1 m and 2 m respectively, and a slant height 3.6 m.

A

6.533 m^3 (p. 64)

19
Q

Set 4 Problem 48: The volume of a square prism is numerically equal to its lateral area. Calculate the length of the side of the base if its height is not equal to the length of its base.

20
Q

Set 4 Problem 49: When a solid metal ball is immersed in a pail of paint, it displaces 288pi cu.cm. of the paint. If the ball will be painted, what is the total area that needs painting?

A

144pi (p. 67)

21
Q

Set 4 Problem 49: When a solid metal ball is immersed in a pail of paint, it displaces 288pi cu.cm. of the paint. If the ball will be painted, what is the total area that needs painting?

A

144pi (p. 67)

22
Q

Set 5 Problem 40: A spherical wedge has a radius of 2 m and a central angle of 80°. Find the volume of the spherical wedge.

A

7.45 m^3 (p.84)

23
Q

Set 5 Problem 59: A rectangular piece of alloy 4 cm by 5 cm by 8 cm is melted and recast into a shape of a pyramid with a square base and height 12 cm. Find the measure of the edge of the base.

A

6.32 cm (p.86)

24
Q

Set 6 Problem 9: The altitude of a cone is 5 ft. A smaller cone is cut from the cone by a plane 2 ft from the vertex and parallel to the base. If the volume of the smaller cone is 24 ft^3, what is the volume of the larger cone?

A

375 ft^3 (p.95)

25
Set 6 Problem 29: Find the percentage increase in the volume of a cube when its side is increased by 50%.
237.5% (p.98)
26
Set 6 Problem 52: Find the volume of a regular octahedron whose edge measures 8 cm each.
241.36 cm^3 (p.102)
27
Set 6 Problem 68: A convenience store sells milkshake in a container comprising of a cylinder with the upper portion surmounted by a hemisphere. If the height of the cylindrical portion is 6 in and the radius 2 in, find the volume of the container.
92.15 in^3 (p. 102)
28
Set 7 Problem 3: A conical vessel with horizontal bottom base is filled with water to three-fourths of its height. Compute the ratio of the volume of water to the volume of the vessel.
63/64 (p.111)
29
Set 7 Problem 4: A truncated prism has a horizontal triangular base with edges 10 cm, 15 cm, and 17 cm. The lateral edges are perpendicular to the plane of the base and measure 6 cm, 8 cm, and 10 cm, respectively. Compute the volume of the truncated prism.
595.66 cm^3 (p.111)
30
Set 7 Problem 33: The volumes of 2 spheres are in the ratio 27:343 and the sum of their surface areas is 18,221.23739 cm^2. Compute the radius of the smaller sphere.
15 cm (p.116)
31
Set 7 Problem 60: Compute the volume of the solid bounded by a circular base of radius 5 cm if every section perpendicular to a fixed diameter of the base is an isosceles right triangle with the hypotenuse on the base.
166.67 cm^3 (p. 120)
32
Set 7 Problem 67: The bases of a right prism are pentagons with sides 8 cm each. Find the distance between the bases if the volume is 1,182.64 cm³.
10.74 cm (p.122)
33
Set 8 Problem 56: The volumes of a sphere and a right circular cylinder are equal and the diameter of the sphere equals the diameter of the base of the cylinder. Determine the altitude (h) of the cylinder in terms of the diameter (D) of the sphere.
2/3D (p.137)
34
The volume of a square pyramid is 384 m^3, and its altitude is 10 m. Set 8 Problem 60: How long is an edge of the base?
10.73 m (p.138)
35
The volume of a square pyramid is 384 m^3, and its altitude is 10 m. Set 8 Problem 61: Compute the length of the lateral edge.
12.55 m (p.138)
36
The volume of a square pyramid is 384 m^3, and its altitude is 10 m. Set 8 Problem 62: Compute the total surface area of the pyramid.
358.7 m^2 (p.138)
37
Set 9 Problem 56: A spherical wedge has a radius of 2.5 m and a volume of 7.86 m^3. Compute the area of its lune.
9.45 cm^2 (p.154)
38
A regular tetrahedron has its edge equal to 10 cm. Set 9 Problem 58: Compute the volume of the tetrahedron.
117.85 cm³ (p.154)
39
A regular tetrahedron has its edge equal to 10 cm. Set 9 Problem 59: Compute the altitude of the tetrahedron.
8.166 cm (p.154)
40
A regular tetrahedron has its edge equal to 10 cm. Set 9 Problem 60: Compute the radius of the sphere inscribed in the tetrahedron.
2.04 cm (p.154)
41
Set 10 Problem 37: Find the volume of a conoid with base radius 2 m and altitude 3 m.
6pi cubic units (p.168)
42
Set 10 Problem 65: A spherical sector is cut from a sphere of radius 17 cm. If the zone has a radius of 12 cm, compute the volume of the spherical sector.
3,002 cm^3 (p.173)

reaY eht fo naicitamehtaM (26 decks)

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