1. The surface area of a cube with side 'a' is:
a) a^2
b) 6a^2
c) a^3
d) 12a
Answer:
b) 6a^2
Explanation:
A cube has six equal faces. Each face has an area of a^2. So, total surface area = 6a^2.
2. The volume of a cylinder with radius 'r' and height 'h' is:
a) πr^2h
b) 2πrh
c) πr^3
d) πh^2
Answer:
a) πr^2h
Explanation:
The volume of a cylinder is given by the base area multiplied by the height: πr^2h.
3. The curved surface area of a cone with slant height 'l' and base radius 'r' is:
a) πrl
b) πr^2
c) ⅓πr^2h
d) 2πr^2
Answer:
a) πrl
Explanation:
Curved surface area of a cone is given by πrl.
4. The volume of a sphere with radius 'r' is:
a) 2/3 πr^3
b) 4/3 πr^3
c) πr^2
d) 4πr^2
Answer:
b) 4/3 πr^3
Explanation:
The volume of a sphere is 4/3 πr^3.
5. The total surface area of a cylinder with radius 'r' and height 'h' is:
a) 2πrh
b) πr^2 + 2πrh
c) 2πr(r+h)
d) πr^2h
Answer:
c) 2πr(r+h)
Explanation:
Total surface area includes two bases and the curved surface: 2πr^2 + 2πrh = 2πr(r+h).
6. A cone and a cylinder have the same base and the same height. The ratio of their volumes is:
a) 1:1
b) 1:2
c) 1:3
d) 2:3
Answer:
c) 1:3
Explanation:
Volume of cone = ⅓πr^2h and volume of cylinder = πr^2h. Their ratio is 1:3.
7. If the radius of a sphere is doubled, its volume becomes:
a) Twice
b) Thrice
c) Four times
d) Eight times
Answer:
d) Eight times
Explanation:
New volume = 4/3 π(2r)^3 = 8 times the original volume.
8. The height of a cylinder with base radius 'r' and volume 'V' is:
a) V/πr^2
b) V/2πr
c) 2V/πr^2
d) πr^2/V
Answer:
a) V/πr^2
Explanation:
Volume of cylinder = πr^2h. Therefore, h = V/πr^2.
9. The volume of a cube with edge 'a' is:
a) a^2
b) 6a^2
c) a^3
d) 3a
Answer:
c) a^3
Explanation:
Volume of cube = a x a x a = a^3.
10. The slant height of a cone with base radius 'r' and height 'h' is:
a) √(r^2 + h^2)
b) r + h
c) rh
d) r^2 + h^2
Answer:
a) √(r^2 + h^2)
Explanation:
By Pythagoras theorem, slant height^2 = r^2 + h^2. So, slant height = √(r^2 + h^2).