Total Surface Area of a Cuboid

Q. Each edge of a cube is increased by $50\%$, then percentage increase in its surface area =.

1. $125\%$
2. $110\%$
3. $150\%$

Q.

Which three-dimensional figure has $5$ faces, $8$ edges, and $5$ vertices?

1. cube

2. cylinder

3. rectangular pyramid

4. cuboid

Q.

A cuboid is $12cm$ long, $9cm$ broad and $8cm$ high. Its total surface area is
$\left(a\right)864c{m}^2\left(b\right)552c{m}^2\left(c\right)432c{m}^2\left(d\right)276c{m}^2$

Q.

Three cubes each of side $5cm$ are joined end to end. Find the surface area of the resulting cuboid

Q.

The dimensions of a room are $8m\times 6m\times h.$ It has two doors each of size $2m\times 1m$ and one almirah of size $3m\times 2m.$ The cost of covering the walls by wallpaper which is $40cm$ wide at $Rs.1.25$ per metre is $Rs.\mathrm{362.50.}$ Find height.

Q.

Two cube each of 10 cm edge are joined end to end. Find surface area of resulting cuboid

Q.

Find the ratio of the total surface area and lateral surface area of a cube.

Q.

If the length of a diagonal of a cube is $8\sqrt{3}cm,$ then its surface area is

1. $512c{m}^2$

2. $192c{m}^2$

3. $768c{m}^2$

4. $384c{m}^2$

Q. The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of the wood is 5 mm. If the empty box weighs 3.15 kg, then the weight of $1c{m}^3$ of wood is ________.

1. 7 grams

2. 15 grams

3. 10 grams

4. 1 grams

Q.

The surface area of a cuboid is $1300c{m}^2.$ If its breadth is 10 cm and height is 20 cm, find its length.

Q. Question 4
The paint in a certain container is sufficient to paint an area equal to $9.375m^2$. How many bricks of dimensions $22.5cm\times 10cm\times 7.5cm$ can be painted out of this container?

Q.

A wall in Marcuss bedroom is $8\frac{2}{5}$ $\mathrm{feet}$ high and $18\frac{1}{3}$ $\mathrm{feet}$ long. If he paints $\frac{1}{2}$ of the wall blue, how many $\mathrm{square}\mathrm{feet}$ will be blue?

Q.

The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

Q.

The total surface area of a rectangular box of dimensions a, 2a and 3a is

1. 12a²

2. 22a²

3. 24a²

4. 20a²

Q. Find the value of x and state which of the given statement is/are required for it.
I. The L.C.M of x and 18 is 36.
II. The H.C.F of x and 18 is 2.

1. 2 only statement-II is required
2. 1, only statement-I is required
3. 4, statement I and II both are required
4. None of these

Q. Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.

Q.

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes is

1. 7:9

2. 49:81

3. 9:7

4. 27:23

Q.

A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs 5 per metre sheet, sheet being 2 m wide.

Q. Find the curved surface area and total surface area of a hemisphere of radius 21cm.

1. CSA = $2772c{m}^2$, TSA = $4158c{m}^2$
2. CSA = $2772c{m}^2$, TSA = $4676c{m}^2$
3. CSA = $2079c{m}^2$, TSA = $74564c{m}^2$
4. CSA = $2126c{m}^2$, TSA =$4253c{m}^2$

Q.

Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?

Q.

_________ surface area of room $=$ area of $4$ walls.

Q.

Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

Q.

$\text{If V is the volume of a cuboid of dimensions a, b, c and S is its surface ara then prove that}\frac{1}{V}=\frac{2}{S}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}).$

Q.

What is the surface area of the cuboidal box which is open at the top, if:
$l=$ length of the cuboid,
$b=$ breadth of the cuboid and
$h=$ height of the cuboid

1. $2(lb+bh+lh)$

2. $2lb+2bh+hl$

3. $2lb+bh+2hl$

4. $lb+2bh+2hl$

Q.

Question 82

At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

Q.

A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height $h$ and radius $r$ are related by

1. $2h=r$

2. $h=4r$

3. $h=2r$

4. $h=r$

Q.

The length, width and height of rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is $48c{m}^3,$ the total surface area of the box is

1. $27c{m}^2$

2. $44c{m}^2$

3. $32c{m}^2$

4. $88c{m}^2$

Q. Question 1
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see Fig. 13.31). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per $c{m}^2$ and the rate of painting is 10 paise per $c{m}^2$ find the total expenses required for polishing and painting the surface of the bookshelf.

Q. Directions: In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion: Two equal cubes are placed adjacent in a row. The ratio of total surface area of the new cuboid to that of the sum of the surface areas of two cubes is 5 : 6

Reason: Surface Area of a cube is $6sid{e}^2$.

1. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
2. Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
3. Assertion (A) is true but reason (R) is false.
4. Assertion (A) is false but reason (R) is true.

Q.

Find the lateral surface area and total surface are of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.