Q. A cone and a cylinder have the same base radius and height. How do their volumes compare?
A.
Cone has half the volume of the cylinder
B.
Cone has the same volume as the cylinder
C.
Cone has double the volume of the cylinder
D.
Cone has one-third the volume of the cylinder
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Solution
Volume of cone = (1/3)πr²h; Volume of cylinder = πr²h. Therefore, cone's volume is one-third of the cylinder's volume.
Correct Answer:
A
— Cone has half the volume of the cylinder
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Q. A cone has a base radius of 2 cm and a height of 6 cm. What is the volume of the cone?
A.
8π cm³
B.
12π cm³
C.
4π cm³
D.
16π cm³
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Solution
Volume of a cone = (1/3)πr²h = (1/3)π(2)²(6) = (1/3)π(4)(6) = 8π cm³.
Correct Answer:
B
— 12π cm³
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Q. A cone has a base radius of 2 m and a height of 6 m. What is its surface area?
A.
16π
B.
20π
C.
24π
D.
28π
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Solution
The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(r² + h²) = √(2² + 6²) = √40. Thus, SA = π(2)(2 + √40) = 20π.
Correct Answer:
B
— 20π
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Q. A cone has a base radius of 3 m and a height of 4 m. What is the surface area of the cone?
A.
15π
B.
18π
C.
21π
D.
24π
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Solution
The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(3² + 4²) = 5, so SA = π(3)(3 + 5) = 24π.
Correct Answer:
C
— 21π
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Q. A cone has a base radius of 4 cm and a height of 9 cm. What is its volume?
A.
12π
B.
36π
C.
48π
D.
72π
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Solution
The volume of a cone is given by V = (1/3)πr²h. Here, r = 4 and h = 9, so V = (1/3)π(4)²(9) = 48π.
Correct Answer:
B
— 36π
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Q. A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area?
A.
50π cm²
B.
65π cm²
C.
70π cm²
D.
80π cm²
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Solution
The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(5² + 12²) = 13, so SA = π(5)(5 + 13) = 90π cm².
Correct Answer:
B
— 65π cm²
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Q. A cylinder has a height of 10 cm and a volume of 100π cm³. What is the radius of the base?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
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Solution
Using the volume formula V = πr²h, we have 100π = πr²(10). Thus, r² = 10, so r = √10 cm.
Correct Answer:
B
— 3 cm
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Q. A cylinder has a height of 10 cm and a volume of 200π cm³. What is the radius of the base?
A.
4 cm
B.
5 cm
C.
6 cm
D.
7 cm
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Solution
Using the volume formula V = πr²h, we have 200π = πr²(10). Thus, r² = 20, so r = √20 = 4.47 cm.
Correct Answer:
B
— 5 cm
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Q. A cylinder has a volume of 100π cm³ and a height of 10 cm. What is the radius of the base?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
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Solution
Volume = πr²h. Therefore, 100π = πr²(10) => r² = 10 => r = √10 ≈ 3.16 cm.
Correct Answer:
C
— 4 cm
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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the total surface area of the tank (including the top and bottom)?
A.
56.52 m²
B.
94.25 m²
C.
75.40 m²
D.
37.68 m²
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Solution
Total surface area = 2πr(h + r) = 2π(3)(5 + 3) = 2π(3)(8) = 48π ≈ 150.8 m².
Correct Answer:
B
— 94.25 m²
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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the volume of the tank in cubic meters?
A.
45π
B.
30π
C.
15π
D.
60π
Show solution
Solution
The volume of a cylinder is given by the formula V = πr²h. Here, r = 3 and h = 5, so V = π(3)²(5) = 45π.
Correct Answer:
A
— 45π
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Q. A hemisphere has a radius of 3 cm. What is its volume?
A.
18π cm³
B.
27π cm³
C.
36π cm³
D.
9π cm³
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Solution
Volume of a hemisphere = (2/3)πr³ = (2/3)π(3)³ = (2/3)π(27) = 18π cm³.
Correct Answer:
A
— 18π cm³
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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is its volume?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
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Solution
Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. A rectangular prism has dimensions 3 m, 4 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(3*4 + 3*5 + 4*5) = 2(12 + 15 + 20) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 3 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*3 + 4*5 + 3*5) = 2(12 + 20 + 15) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 5 m, and 6 m. What is its surface area?
A.
94 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*5 + 4*6 + 5*6) = 94 m².
Correct Answer:
A
— 94 m²
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Q. A sphere has a radius of 7 cm. What is its surface area?
A.
154 cm²
B.
196 cm²
C.
308 cm²
D.
616 cm²
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Solution
Surface area of a sphere = 4πr² = 4π(7)² = 4π(49) = 196 cm².
Correct Answer:
B
— 196 cm²
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Q. If a cube has a volume of 64 cubic centimeters, what is the length of one side of the cube?
A.
4 cm
B.
8 cm
C.
16 cm
D.
2 cm
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Solution
Volume of a cube = side³. Therefore, side = ∛64 = 4 cm.
Correct Answer:
A
— 4 cm
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Q. If a sphere has a volume of 288π cubic centimeters, what is its radius?
A.
6 cm
B.
8 cm
C.
9 cm
D.
10 cm
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Solution
The volume of a sphere is given by V = (4/3)πr³. Setting (4/3)πr³ = 288π, we find r³ = 216, thus r = 6 cm.
Correct Answer:
B
— 8 cm
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Q. If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.
Correct Answer:
B
— It doubles
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Q. If the radius of a sphere is halved, how does its volume change?
A.
It remains the same
B.
It doubles
C.
It halves
D.
It reduces to one-eighth
Show solution
Solution
Volume of a sphere = (4/3)πr³. If radius is halved, volume becomes (4/3)π(1/2)³ = (4/3)π(1/8) = (1/6)π, which is one-eighth of the original volume.
Correct Answer:
D
— It reduces to one-eighth
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Q. If the surface area of a cube is 216 square meters, what is the length of one side of the cube?
A.
6 meters
B.
9 meters
C.
12 meters
D.
15 meters
Show solution
Solution
The surface area of a cube is given by the formula SA = 6a². Setting 6a² = 216, we find a² = 36, thus a = 6 meters.
Correct Answer:
B
— 9 meters
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Q. If the surface area of a cylinder is 150π cm² and the height is 10 cm, what is the radius?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the surface area of a cylinder is 150π cm² and the height is 5 cm, what is the radius?
A.
5 cm
B.
3 cm
C.
4 cm
D.
2 cm
Show solution
Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(5 + r), we find r = 4 cm.
Correct Answer:
C
— 4 cm
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Q. What is the total surface area of a sphere with a radius of 7 cm?
A.
49π
B.
98π
C.
144π
D.
196π
Show solution
Solution
The total surface area of a sphere is given by SA = 4πr². Here, r = 7, so SA = 4π(7)² = 196π.
Correct Answer:
B
— 98π
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Q. What is the volume of a cube with a side length of 4 cm?
A.
16 cm³
B.
32 cm³
C.
64 cm³
D.
80 cm³
Show solution
Solution
The volume of a cube is given by V = a³. Here, V = 4³ = 64 cm³.
Correct Answer:
C
— 64 cm³
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