Total Surface Area of a Cuboid

Q. A cube of lead which adges measuring 6 cm is melted and formed into 27 equal cubes what will be the length of the edges of the new cubes?

Q. The smallest number by which 5400 must be multiplied so that it becomes a perfect cube:

1. 2
2. 3
3. 10
4. 5

Q.

Prove that if a number is tripled, then it's cube is 27 times the cube of the given number.

Q.

An aquarium is in the form of a cuboid whose external measures are $80cm\times 30cm\times 40cm$. The base side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?

Q.

A river $2m$ deep and $45m$ wide is flowing at the rate of $3km$ per hour. Find the volume of water that run into the sea per minute.

Q.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? Volume : $3x^2-12x$

Q.

Find the number of coins , 1.5cm in diameter and 2mm thick, to be melted to form a right circular cylinder of radius 2.25cm and height 10cm.

Q.

Question 3
A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.

Q.

How many bricks of size $22cm\times 10cm\times 7cm$ are required to construct a wall 11 m long, 3.5 m high and 40 cm thick, if the cement and sand used in the construction occupy $\left(\frac{1}{10}\right)th$ part of the wall?

Q.

Question 88

A square sheet of paper is converted into a cylinder by rolling it along its side. What is the ratio of the base radius to the side of the square?

Q.

The distance between the two towns is $300$ km. Two cars start simultaneously from these towns and move towards each other. The speed of one car is more than the other by $7$ km per hour. If the distance between the cars after $2$ hours is $34$ km, find the speed of the cars.

Q.

Various modes of transport used by 1260 students in a given school are given below :

$\begin{array}{ccccc}\text{School bus}& \text{Private bus}& \text{Bicycle}& \text{Rickshaw}& \text{On foot}\\ 350& 245& 210& 175& 280\end{array}$

Represent the above data by a pie char.

Q.

A cuboidal water tank is $6m$ long, $5m$ wide and $4.5m$ deep.

How many liters of water can it hold? ($1m^3=1000l$)

Q.

Question 5

Write the correct answer from the given four options.

How many natural numbers lie between $5^2$ and $6^2$?

a) 9
b) 10
c) 11
d) 12

Q.

A rectangular sheet of the fixed perimeter with sides having their lengths in the ratio $8:15$ is converted into an open rectangular box by folding after removing squares of the equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are

1. $24$

2. $32$

3. $45$

4. $60$

Q.

Find the surface area and volume of a rectangular pyramid.

Q.

The formula to find total surface area of a cuboid is__________.

1. 2 (lb + bh + hl)

2. 2 (lb x bh x hl)

3. 2h (l + b)

4. 2 lb (bh + hl)

Q.

Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:

(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm

(ii) length = 15 in, breadth = 6 in and height = 9 dm

(ill) length = 24 m, breadth = 25 cm and height = 6 m

(iv) length tr- 48 cm. breadth = 6 dm and height = 1 In

Q.

A cubical solid aluminum ($K=-V\left(\frac{dP}{dV}\right)=70GPa$) block has an edge length of $1m$ on the surface of the earth. It is kept on the floor of a $5km$ deep ocean. Taking the average density of water and the acceleration due to gravity to be ${10}^{3}kg{m}^{-3}$and $10m{s}^{-2}$ respectively, the change in the edge length of the block in $mm$ is _____.

Q.

Find the cost of painting a tank of dimension $3m\times 2m\times 1.5m$ at ₹20 per square metre .

Q.

A well 14m inside diameter is dug 15m deep. Earth taken out is spread all around to a wridth of 7m to form a embankment. Find the height of the embankment.

Q.

A cylindrical vessel , without lid, has to be tin coated on its its both sides. If the radius of the base is $70cm$ and it's height is $1.4m$, calculate the cost of tin coating at the rate of $Rs.3.50$ per $1000c{m}^2$.

Q. How many persons can be accommodated in a hall of length 16m , breadth 12.5m , and height 4.5m , assuming that 3.6 m³ of air is required for each person?

Q. A rectangular swimming pool 30m long, 20m wide, 1.5m deep is to be tiled.If each tile is 50m ×50m, how many times will be required. (Remember there is no roof.)

Q. The length, breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of the
cuboid is 1926 sq. cm. find the surface area of the cuboid.

Q. Surface area of one face of a cube is 64 cm. Find the volume of this cube.

Q.

The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid. [3 MARKS]

Q.

Which of the following is a polyhedron?

1. Cuboid

2. Sphere

3. Cone

4. Cylinder

Q. How many rectangular faces does a rectangular cuboid have?

1. 5
2. 3
3. 4
4. 6

Q. Swimming pool is 20 m in length 15 m in breadth and 4 m in depth find the cost of cementing its floor and four walls at the rate 6 rupees 12 per metre square