Shape Conversion of Solids

Q.

Question 22

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is
(a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Q. How many solid cubes of 6-cm edge can be cut out of a solid cube of 24-cm edge?

1. 32
2. 64
3. 128
4. 256

Q.

Question 22

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is
(a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Q. How many cubes of edge 4 cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively

Q. Question 6
Describe how the two figures below are alike and how they are different. Which box has larger lateral surface area?

Q. Which 3D solids have no faces, no edges and no vertices?

1. Cylinder
2. Cube
3. Pyramid
4. Sphere

Q.

Question 24

The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is
a) 1 : 6
b) 1 : 9
c) 1 : 3
d) 2 : 9

Q. The diagram below shows a cube with sides of length 30 cm. A smaller cube with sides of length 5 cm has been cut out of the larger cube. What is the volume of the shape that is left?

1. $26875c{m}^3$
   
2. $2675c{m}^3$
3. $28765c{m}^3$
4. $275c{m}^3$

Q.

Question 51

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

Q. If two cubes of side 6 cm are joined end to end, find the total surface area ($c{m}^2$) of the resultant solid.

1. 360

Q. A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Q. The radius of a right circular cone $A$ is $\frac{1}{5}$ of the radius of right circular cone $B$, and the height of right circular cone A is $\frac{1}{4}$ of the height of right circular cone B. Calculate the ratio of the volume of right circular cone A to the volume of right circular cone B.

1. $\frac{1}{16}$
2. $\frac{1}{25}$
3. $\frac{1}{64}$
4. $\frac{1}{100}$
5. $\frac{1}{80}$

Q. The measures of a solid cuboid are $66cm,42cm$ and $21cm$ respectively. How manyspheres with diameter $4.2cm$ each can be recasted by melting it.

Q. The amount of water required to fill the given cuboidal fish tank with water is 20 ft$^3$.

Q.

Question 103

Three cubes each of side 10 cm are joined end to end. Find the surface area of the resultant figure.

Q.

How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

1. 550

2. 350

3. 500

4. 400

Q. $A$ took $15$ seconds to cross a rectangular field diagonally walking at the rate of $52$ m/min and B took the same time to cross the same field along its sides, walking at the rate of $68$ m/min. The area of the field is:

1. $60m^2$
2. $30m^2$
3. $50m^2$
4. $40m^2$

Q.

Question 52

Two cylinders of same volume have their radii in the ratio 1 : 6. Then, ratio of their heights is ___

Q. Two cubes of side $6cm$ are joined end to end to form a cuboid. Then the volume of the resulting cuboid in ${cm}^3$ is

1. $216$
2. $116$
3. $432$
4. $418$

Q. Ice cream is filled to the brim in a cylindrical container of radius 20 cm and height 60 cm. How many cones of radius 3 cm and height 10 cm are needed to hold this ice cream?

Q. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
(a) 6 cm (b) 8 cm
(c) 23 cm (d) 24 cm

Q.

A man makes a cuboid of plastic of dimension 5cm, 2cm, 5cm. Find the volume to be added to the original cuboid to form a perfect cube? [2 MARKS]

Q. How many solid spheres of radius 1 cm will be formed by melting a solid metallic sphere of radius 8 cm?

Q. Number of cylindrical cups(r =6 cm & h =16 cm) that can be filled from a cylindrical can (r =30 cm & h = 64 cm) is .

1. 200
2. 100
3. 300

Q. Water in a cylindrical tank of a diameter $4m$ and height $10m$ is released through a cylindrical pipe of diameter $10cm$ at the rate of $2.5Km/hr$. How much time will it take to empty the half of the tank? Assume that the tank is full of water to begin with.

1. $3hr$ $12min$
2. $2hr$ $12min$
3. $3hr$ $22min$
4. None of these