Cuboid

Q. A cuboid is formed by joining two cubes of volume $216c{m}^3$. Total surface area of the cuboid will be .

1. $180c{m}^2$
2. $90c{m}^2$
3. $200c{m}^2$
4. $360c{m}^2$

Q.

A paper is rectangular in shape with negligible thickness. A stack of papers is arranged one above the other.

S1 : The resulting figure is three dimensional.

S2 : The figure is called a cuboid.

1. S1 is false but S2 is true

2. S1 is true but S2 is false

3. S1 and S2 are true

4. S1 and S2 are false

Q. If the inner dimensions of a cuboidal box are 50 cm $\times$ 40 cm $\times$ 30 cm, then the length of the longest rod that can be placed in the box is

1. $50\text{cm}$
2. $50\sqrt{2}\text{cm}$
3. $50\sqrt{3}\text{cm}$
4. $120\text{cm}$

Q. Question 87

Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?

Q.

Five balls of different colors are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

1. $50$

2. $100$

3. $150$

4. $200$

Q.

Cuboids can be formed by stacking ___ .

1. Rectangle/Rectangles

2. Squares

3. Triangles

4. Trapezium

Q. Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

1. $4\pi r^2$
2. $3\pi r^2$
3. $\frac{4}{3}\pi r^3$
4. $\frac{2}{3}\pi r^3$

Q.

Find AB in the given figure

1. 10√3

2. 20√3

3. 30√3

4. √3

Q. The ratio of the surface area of two spherical balls of radii 3 cm and 4 cm = .

1. 9:16
2. 27:64
3. 3:4
4. 9:64

Q. A cuboid-shaped box has dimensions 4 m×3 m×2 m.Match the no. of boxes of given volume that can fit in the box.

1. 120
2. 80
3. 60
4. 40

Q.

Question 156

Sanchay put a 1 cm stick of gum through a $(1\times 3^{-2})$ machine. How long was the stick when it came out ?

Q. A match box measures 4 cm $\times$ 2.5 cm $\times$ 1.5 cm. Which of the following does not represent the volume of a packet containing 12 such boxes?

1. $180c{m}^3$
2. $72\times 2.5c{m}^3$
3. $12\times 15c{m}^3$
4. $(4\times 2.5\times 1.5)c{m}^3$

Q.

A metal sheet of width $1m$ is kept in a roll. A worker needs to make a box of dimensions $50cm\times 30cm\times 45cm$. Find the length of the sheet required to make the box.

1. $1m$

2. $1.02m$

3. $112cm$

4. $95cm$

Q.

A metal sheet of width $1m$ is kept in a roll. A worker needs to make a box of dimensions $50cm\times 30cm\times 45cm$. Find the length of the sheet required to make the box.

1. $112cm$

2. $1.02m$

3. $95cm$

4. $1m$

Q.

All cuboids are cube.

1. False

2. True

Q. A cylinder of circumference $8$ cm and length $21$cm rolls without sliding for $4\frac{1}{2}$ seconds at the rate of $9$ complete rounds per second. Find the area covered by the cylinder in $4\frac{1}{2}$ seconds.

1. $6104$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
2. $6804$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
3. $6404$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
4. $6204$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.

Q. Each edge of a cube is increased by 50%. The per cent of increase in the surface area of the cube is

1. 50
2. 125
3. 750
4. 300

Q. A tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, then find the cost of canvas needed to make the tent if the canvas is available at the rate of ₹500 per sq. metres. [Use $\pi =\frac{22}{7}$]

Q. The base area, side area and front area of a rectangular box are known. The product of these areas is equal to ___.

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

Q. Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

1. $\frac{4}{3}\pi r^3$
2. $4\pi r^2$
3. $\frac{2}{3}\pi r^3$
4. $3\pi r^2$

Q. Find the surface area of a sphere of radius $14$ cm.

1. $2464{cm}^2$
2. $1446c{m}^2$
3. $2446c{m}^2$
4. $2664c{m}^2$

Q. The volume of water required to fill half a tank of length 3 m, breadth 4 m and height 5 m is .

1. 30

Q. The curved surface area of a right circular cylinder of height 14 cm is 88 $c{m}^2$. The radius of the cylinder is

1. $2$ cm
2. $1$ cm
3. $4$ cm
4. $3$ cm

Q.

A rectangular cardboard of dimension 20 m $\times$ 10 m is placed on a table. 4 squares of side 2.5 m are cut out from the corners and the 4 sides are folded . Find the surface area of the resulting figure which is to be painted on all the sides.

1. 175 $m^2$

2. 155 $m^2$
3. 180 $m^2$
4. 100 $m^2$

Q. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. [3 Marks]

Q. A jeweler makes beads for a bracelet by melting silver into spherical molds. Each mold has a diameter of $1$ centimeter. After the silver hardens, the jeweler drills a small cylindrical hole through the center of the bead for the chain as shown. The drill bit has a diameter of $4$ millimeters. If the jeweler strings a total of $15$ beads on an elastic band, what is the approximate volume of silver, in cubic centimeters, on the bracelet?

1. $\frac{19}{150}\pi$
2. $\frac{1}{6}\pi$
3. $\frac{19}{10}\pi$
4. $\frac{5}{2}\pi$

Q. Suppose that there is a conical strainer as shown in the given figure. The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 ${cm}^2$ of strainer has an average of 8 tiny holes. Then find the total number of holes in the entire strainer.

Q.

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1 m and base radius 3.5 cm?
(Take π=22/7)

1. $1100{cm}^2$
2. $3300{cm}^2$
3. $2200{cm}^2$
4. $1500{cm}^2$

Q. Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

1. $\frac{2}{3}\pi r^3$
2. $3\pi r^2$
3. $4\pi r^2$
4. $\frac{4}{3}\pi r^3$

Q. The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?