Total Surface Area of a cube

Q.

If each edge of a cube is increased by $50\%$, the percentage increase in its surface area is

1. 50%

2. 75%

3. 100%

4. 125%

Q.

The volume of a cylindrical tin can with a top and a bottom is $16\mathrm{\pi }$ cubic inches.

If a minimum amount of tin is to be used to construct the can, what must be the height of the can in inches $?$

1. Height$=2\sqrt[3]{2}$ inches.

2. Height$=2\sqrt[3]{4}$ inches.

3. Height$=4$ inches.

4. Height$=8$ inches

Q.

The volume of a cube whose surface area is $96c{m}^2,$ is

1. $64c{m}^3$

2. $16\sqrt{2}c{m}^3$

3. $32c{m}^3$

4. $216c{m}^3$

Q. If the height of a sphere is 20 cm, then the total surface area of the sphere is

1. $800\pi c{m}^2$
2. $1600\pi c{m}^2$
3. $400\pi c{m}^2$
4. $600\pi c{m}^2$

Q.

Find the surface area of a sphere of diameter $14cm$.

Q.

The wedge is one-eighth of the wheel of cheese

(a) Find the surface area of the cheese before it is cut.

(b) Find the surface area of the remaining cheese after the wedge is removed. Did the surface area increase, decrease, or remain the same?

Q.

The total surface area of a cube is $1176c{m}^2$. Find its volume.

Q. A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and one of the cuboid.

1. 2 : 1
2. 1 : 2
3. 2 : 3
4. 3 : 2

Q.

Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: $P$ units.

Q.

The internal length, breadth and height of a rectangular box A is20 cm, 18 cm and 15 cm respectively and that of the box B are 18cm, 12cm and 5 cm respectively. The volume of box A is how many times that of B?

1. 5

2. 4

3. 6

4. 3

Q.

The length of an edge of a cube is $l$. Find the formula for the sum of lengths of all the edges of the cube.

Q. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also find the ratio between their surface areas.

Q.

Find the edge of a cube whose surface area is 432 $m^2.$

Q.

If each edge of a cube of surface area ${}^{\prime }{S}^{\prime }$ is doubled, then the surface area of the new cube is

1. $8S$

2. $2S$

3. $6S$

4. $4S$

Q.

$500$ persons are taking a dip into a cuboidal pond which is $80\mathrm{m}$ long and $50\mathrm{m}$ broad. What is the rise of water level in the pond, if the average displacement of the water by a person is $0.04{\mathrm{m}}^3$?

Q.

The lateral surface area of a cube is 100 m². The volume of the cube is:

1. 100 m³

2. 25 m³

3. 125 m³

4. 1000 m³

Q. Question:

Question 8
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Mathematics Surface Areas and Volumes Volume of Solids
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Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

Q.

Sam's cubicle is exactly in the shape of a cube of side 6 m. If it is a closed cubicle, then the total surface area of the cubicle ignoring its thickness is _______.

1. $144m^2$ ​

2. $196m^2$ ​

3. $216m^2$ ​

4. $256m^2$ ​

Q.

A room is $5\text{m}40\text{cm}$ long and $4\text{m}50\text{cm}$ broad. Its area is:

1. $\begin{array}{rcl}& & 24.3{\text{m}}^2\end{array}$

2. $34.3{\text{m}}^2$

3. $25{\text{m}}^2$

4. $98.01{\text{m}}^2$

Q.

The total surface area of a cone shaped Christmas tree of with base radius 6 m and height 8 m is 188.44 sq. meter. Is the given statement is true? (Take π=$\frac{22}{7}$)

1. True

2. False

Q.

The dimensions of the floor of a rectangular hall are $4m\times 3m$. The floor of the hall is to be fully with $8cm\times 6cm$ rectangular tiles without breaking tiles to smaller size. Find the number of tiles required.

Q. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Q.

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. [3 MARKS]

Q.

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

Q. Find the total surface area of cubes having the following sides.

Q.

If each edge of a cube is increased by $50\%$ then percentage increase in its surface area is

(a) $50\%$ (b) $75\%$ (c) $100\%$ (d) $125\%$

Q. What is the formula for the total surface area of a cube?

Q.

Two cubes have their volumes in the ratio 1 :27.The ratio of their surface areas is

(a ) 1:3 (b) 1:8 (c) 1:9 (d) 1:18

Q.

Mary bought a video game as birthday gift to Sam. Sam likes stamp collection and hence Mary wants to cover the video game gift box with square shaped stamps, each of side 2 cm . If the gift box has length, breadth and height as 8 cm, 6 cm and 2 cm respectively, then how many stamps she has to collect so as to cover the entire gift box? [3 MARKS]

Q.

A box with a square base and open top must have a volume of $13,500c{m}^3$ .

Find the dimensions of the box that minimize the amount of material used.

sides of base =___cm

height =____cm