Putting it together: Solids

Q.

Water in a canal, $5.4$ m wide and $1.8$ m deep, is flowing with a speed of $25$ km/hour. How much area can it irrigate in $40$ minutes, if $10$ cm of standing water is required for irrigation ?

Q.

What is the volume of a square pyramid of base edge 10 centimetres and slant height 15 centimetres?

Q.

Without calculating determine which solid has the greater volume. Explain your reasoning.

Q.

Determine the ratio of the largest length of rods that can be fitted in a sphere and cube, given that the sphere exactly fits inside the cube.

1. $\sqrt{3}:1$

2. $1:\sqrt{3}$

3. 1:1

4. 2:1

Q. Question 4
Write ‘True’ or ‘False’ and justify your answer in the following
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is $\frac{4}{3}\pi a^3$

Q. The volume of a cube is 1000 cm³. Find its total surface area.

Q.

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

1. $\pi :6$

2. $6:\pi$

3. $3:\pi$

4. $\pi :3$

Q. The perimeter of one face of a cube is 24 cm.
Find (i) the total area of the 6 faces
(ii) the volume of the cube.

Q. A sphere and cube have equal surface areas. The ratio of their volumes is

1. $\frac{\pi }{6}$
2. $\frac{6}{\pi }$
3. $\sqrt{\frac{6}{\pi }}$
4. $\sqrt{\frac{\pi }{3}}$

Q.

What is the volume of a cube with edges of length 10 m?

1. 1, 000 Cubic Metres

2. 10, 000 Cubic Metres

3. 10 Cubic Metres

4. 100 Cubic Metres

Q. What will be the ratio of volume of cube is to volume of sphere inscribed in the cube?

1. $3:\pi$
2. $6:5$
3. $2:\pi$
4. $6:\pi$

Q. A cube of side 6 cm is cut into a number of cubes, each of side 2 cm. The number of cubes formed is
(a) 6
(b) 9
(c) 12
(d) 27

Q. The perimeter of one face of a cube is 20 cm. Its volume will be:

1. $125c{m}^3$
2. $400c{m}^3$
3. $250c{m}^3$
4. $625c{m}^3$

Q. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

1. $\pi :6$
2. $6:\pi$
3. $\pi :3$
4. $3:\pi$

Q. A cube of side 6 cm is cut into a number of cubes, each of side 2 cm. The number of cubes formed is
(a) 6
(b) 9
(c) 12
(d) 27

Q. Water in a canal, $30dm$ wide and $12dm$ deep is flowing with velocity of $10km/hr$. How much area will it irrigate in $30$ minutes, if $8cm$ of standing water is required for irrigation?

Q. A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in figure. If the edge of each cube is $3cm$, find the volume of the structure built by the child. (in ${cm}^3$)

Q. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Q. How many bricks of 48 cubic units can be stored in a room of dimensions 12 x 4 x 10?

1. 18
2. 15
3. 12
4. 10

Q.

Water in a river 6m wide and 1.5m deep flows with a speed of 10km/hr. How much area will it irrigate in half an hour if 8cm of standing water is needed?

1. 52.45 Hectares

2. 49.25 Hectares

3. 56.25 Hectares

4. 66.76 Hectares

Q. Three iron cubes with edges 3 cm, 4 cm and 5 cm respectively, are melted and cast into a single cube. Find the edge of the bigger cube formed.

1. 18
2. 16
3. 6
4. 8

Q. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

1. $\pi :6$
2. $6:\pi$
3. $3:\pi$
4. $\pi :3$

Q. If we cut a cube of edge 4 cm into n number of cubes of edge 2 cm, what is the possible value of n?

1. 18
2. 9
3. 8
4. 10