Hemisphere

Q. The area of three adjacent faces of a cube is a, b and c. The volume is V. What is the appropriate relation between V and a, b, c?

1. $V^4=abc$
2. V = abc
3. $V^3=abc$
4. $V^2=abc$

Q. Question 9
The length of the longest pole that can be put in a room of dimensions $(10m\times 10m\times 5m)$ is:

A) 15 m
B) 16 m
C) 10 m
D) 12 m

Q. The volumes of the two cubes are in the ratio 64:27. Find the ratio of their surface areas.

1. $16:25$
2. $4:3$
3. $9:16$
4. $16:9$

Q. If each edge of a cube is doubled, then by how many times will its surface area increase?

1. 24 times
2. 2 times
3. 4 times
4. 6 times

Q. If each edge of a cube is doubled, then by how many times will its surface area increase?

1. 24 times
2. 4 times
3. 2 times
4. 6 times

Q. If the volume of a hemisphere is four times its total surface area, then find its radius
(in cm)?

1. 18

Q. The areas of three adjacent faces of a cuboid are $x,y$ and $z.$ If the volume is $V;$ then $:V^2=xyz.$

Q. If each edge of a cube is doubled, then by how many times will its surface area increase?

1. 6 times
2. 2 times
3. 24 times
4. 4 times

Q. A right pyramid is on a regular hexagonal base. Each side of the base is 10 m. Its height is 60 m.The volume of the pyramid is

1. 5196 $m^3$
2. 5200 $m^3$
3. 5210 $m^3$
4. 51220$m^3$

Q. The areas of three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to

1. the volume of the box.
2. twice the volume of the box.
3. the square of the volume of the box.
4. the cube root of the volume of the box.

Q.

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

1. 144 cm³

2. 132 cm³

3. 154 cm³

4. 169 cm³

Q.

What is the volume of water that can be filled in a hemispherical bowl of radius 10 cm? [1 MARK]

Q. A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .

1. $324c{m}^3$
2. $213.4c{m}^3$
3. $516c{m}^3$
4. $981c{m}^3$

Q. The volumes of two hemispheres are in the ratio of 8:27. Find the ratio of their radii.

1. 2:3
2. 3:2
3. 1:3
4. 4:3

Q.

The radius of a hemisphere having total surface area of 1848 sq. cm is 7 cm.

1. True

2. False

Q.

A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid(in $c{m}^2$ ).

1. 332.5 $c{m}^2$

2. 346.8 $c{m}^2$

3. 312.5 $c{m}^2$

4. 320 $c{m}^2$

Q. If a cylindrical vessel has a hemispherical bottom with radius 4 cm and height 15 cm, then its volume is .

1. $686.4c{m}^3$
2. $885.6c{m}^3$
3. $445c{m}^3$
4. $795c{m}^3$