# Grade 8 Volume and Surface Area Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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## (1) Find the Surface Area Of

(a) A cube of side length 5 cm.

(b) A cuboid of dimension

## (2) Find the Surface Area Of

(a) A cylinder of base radius 4 cm and height 10 cm.

## (4) Find the Volume Of

(a) A cube of side length 6 cm.

(b) A cuboid of dimension

(c) A cylinder of base radius 1.4 m and height 2.1 m

(a) Side length

(b) Volume

(a) Height

(b) Volume

(a) Side length

(b) Surface area

## (8) Tick (√) the Correct Option

(a) If each side of a cube is increase to three times, than the surface area of the new cube will be:

## (9) Tick (√) the Correct Option

(a) If each side of a cube is increase to three times, than the Volume of the new cube will be:

## (10) Tick (√) the Correct Option

(a) If the height of a cylinder is increase to three times, than the volume of new cylinder will be:

## (11) Tick (√) the Correct Option

(a) If the height of a cylinder is increase to three times, than the Curved Surface area (CSA) of new cylinder will be:

## (18) a Wooden Box is in the Shape of a Half Cylinder Mounted on a Cuboid as Shown in Figure A Warehouse is Used as a Granary is is the Shape of a Cuboid …

(a) Find its surface area.

## (19) a Wooden Box is in the Shape of a Half Cylinder Mounted on a Cuboid as Shown in Figure A Warehouse is Used as a Granary is is the Shape of a Cuboid …

(a) Find its volume.

## (20) the Internal Radius of a 3 M Long Cylindrical Pipe is 8 Cm. If the Thickness of the Pipe is 0.30 Cm, Find The

(a) Volume of the metal used. (Leave your answer in terms of )

## (21) the Internal Radius of a 3 M Long Cylindrical Pipe is 8 Cm. If the Thickness of the Pipe is 0.30 Cm, Find The

(a) Surface area of the pipe. ( (Leave your answer in terms of )

(22) A cuboid block of dimension is recast into some cylindrical disks of the radius 7cm and height 5cm. find the number of disks formed

## (23) a Hole of Radius 6 Cm is Drilled through a Cubical Block of Side Length 14 Cm at Centre Find

(a) The volume of the solid formed.

## (24) a Hole of Radius 6 Cm is Drilled through a Cubical Block of Side Length 14 Cm at Centre Find

(a) The Surface area of the Solid formed.

(25) A rectangular sheet of dimensions is rolled along its breadth without any overlap to make a cylinder. Find the volume of the cylinder formed.

## (26) a Cylindrical Roller՚s Base Radius is 0.50m and Length is 1.4 Meter Find

(a) Volume of roller

(b) The area covered by the roller in one revolution

(c) The area covered by the roller in 250 revolutions

• A cube has 6 sides.
• And each side is a square having length equal to cube side length.
• Side length of cube is 5 cm given.
• Hence,

• So, Surface area of cube having size 5cm is

• A cuboid having a dimension is
• Means its

• A cylinder of base radius 4 cm and height 10 cm.
• So for cylinder
• And

• Therefore, the surface area of cylinder is .

• A cylinder of base radius 14 ft and height 20 ft
• So for cylinder
• And

• A cube of side length (a)

• Therefore, the volume of cube is .

• A cuboid having a dimension is
• Means its

• Therefore, the volume of cuboid is .

• A cylinder of base radius 1.4 m and height 2.1 m
• So for cylinder
• And

• Therefore, the volume of cylinder is .

• Surface area of cube is .
• If side of a cube is “a” than,

• So , side of a cube is 7 cm

• Volume of a cube having side length (a) is 7 cm.

• Curved area surface of cylinder

• Where “h” is height of cylinder.

• So, height of Cylinder is 6 cm.

• Height of cylinder

• Length of Cuboid (l)
• Suppose Height of Cuboid

• So height of Cuboid is 5 cm.

• Length of Cuboid (l)
• Height of Cuboid (h)

• Suppose side Length of cube is
• So,

• Now, if Side of the cube increase to three times than new side of the cube will be
• So new side length of Cube is

• Hence, the surface area of the new cube will be:

• Suppose side Length of cube is
• So,

• Now, if Side of the cube increase to three times than new side of the cube will be
• So, new side length of Cube is

• Hence, the Volume of the new cube will be:

• Suppose Radius of base circle is
• And Height of cylinder is
• Now, if height of the cylinder increase to three times than its new height will be

• Hence, the volume of the new cylinder will be

• Suppose Radius of base circle is
• And Height of cylinder is

• Now, if height of the cylinder increase to three times than its new height will be

• Hence, the curved surface area of the new cylinder will be

• Suppose Radius of base circle is
• And Height of cylinder is

• Now, if Radius of the cylinder decrease to one third than its new Radius will be
• Now, if height of the cylinder increase to three times than its new height will be

• Hence, the volume of the new cylinder will be

• Suppose Radius of base circle is
• And Height of cylinder is

• Now, if Radius of the cylinder decrease to one third than its new Radius will be
• Now, if height of the cylinder increase to three times than its new height will be

• Hence, The Curved surface area of the New Cylinder will be

• First Container:
• First container is a Cube having size of 6 meter.

• Hence given Cube can Store water.
• Second Container:
• Second Container is a cuboid of Length (l)
• Height (h)

• Hence, the given Cuboid can store water.
• Third Container:
• Third Container is a cylinder having radius (r)
• Height (h)

• Hence the given cylinder can store water
• So, among all three given size container; Cylinder can Store the most water.

• Swimming pool is of a cuboid shape having length (l)
• Depth
• As shown in below figure while we paint the cuboid shape swimming pool than its only 5 is closed one side is open for swimming, so we cannot paint this side.
• So, while we calculate the surface area we consider only 5 side.

• Now,

• Therefore, the cost of painting of cuboid shape Swimming pool is

• Volume of the prism

• Hence , the Volume of the given prism is

• Volume of the prism

• Now, Base area of Prism:
• Base of prism is a square having size 5 cm.

• Length of Prism is 20 cm given.

• Hence , the Volume of the given prism is 5

• Surface area of wooden box

• Surface area of Cuboid:
• Half cylinder is mounted on a cuboid so, while calculating the surface area we consider only 5 side of the cuboid.
• For cuboid length (l)
• And height (h)
• So,

• Surface area of Cylinder.
• Diameter of cylinder ,
• Length (height) of cylinder

• Now, Surface area of wooden box

• So, Surface area of Wooden box is

• Volume of wooden box

• Volume of cuboid:
• For cuboid length (l)
• And height (h)
• So,

• Volume of half cylinder:
• Diameter of cylinder ,
• Length (height) of cylinder

• So, Volume of wooden box

• So, Volume of Wooden box is

• The internal radius of a 3m long cylindrical pipe is 8 cm.
• So,
• So,

• Now, Thickness of pipe is 0.30 cm
• So, New Radius of pipe
• Height remains same.

• Now,

• Surface area of the pipe

• Inner surface area of pipe:
• Height of cylinder (h)

• Outer Surface area of pipe:
• Thickness of pipe is 0.30 cm
• Height of cylinder (h)

• Side Circle Surface area:

• Now,

• So, Surface area of pipe

• A cuboid block of dimension
• Hence,

• This Cuboid is recast into some cylindrical disks having radius

(r)

• And height of that cylinder (h)

• Now,

• So, there can be a “4” complete disc formed after recasting

• Volume of the Solid formed

• Volume of Cube:
• Side (a) of cube is 14cm given

• Volume of Cylinder:
• Height of Cylinder (h)

• Now,

• Surface Area of Solid formed

• Surface Area of Cube:
• Cube having Side (a) of 14 cm

• Cylindrical Surface Area of Cylinder:
• Height of Cylinder (h)

• Circle Area:
• Circle having radius (r) = 6cm

• Surface Area of Solid formed

• A rectangular Sheet Dimension
• So, its Length
• Now, if sheet is rolled along its breadth without any overlap to make a cylinder, than its breadth will be the perimeter of circle formed due to rolled out.

• So, Radius (r) of formed Cylinder is
• And height (h) of formed cylinder

• Radius of cylindrical roller (r)
• Height of Cylindrical roller (h)