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.

(3) Find the Curved Surface Area of a Cylinder of Base Radius 14 Ft and Height 20 Ft

(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

(5) a Surface Area of Cube is 294 Cm2, Find Its

(a) Side length

(b) Volume

(6) the Curved Surface Area of a Cylinder is 792 Cm2. If the Base Radius of the Cylinder is 21 Cm. Find Its (Take Ξ  = 22/7)

(a) Height

(b) Volume

(7) the Volume of a Cuboid of Length 6 Cm and Breadth 9 Cm is 270cm3. Find Its

(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:

(12) if the Radius of a Cylinder is Decrease to One Third and Its Height is Increase to Three Times, Than the Volume of the Cylinder Will Be

(13) if the Radius of a Cylinder is Decrease to One Third and Its Height is Increase to Three Times, Than the Curved Surface Area (CSA) of the Cylinder Will Be

(14) Tick (√) the Container That Can Hold the Most Water. (Each Measurement is in Meter.) (Take Π = 22/7)

Illustration 2 for 14_Tick________the_container_that_can …

(15) Find the Cost of Painting of Cuboid Shape Swimming Pool of Length 10 Meter Breadth 20 Meter and Depth 2 Meter at Rate of β‚Ή 10 Per Square Meter

(16) Find the Volume of below Prism. (Each Measured in Centimetres.)

Illustration 3 for 16_Find_the_volume_of_below_Pri …

(17) Find the Volume of the below Prism. (Each Measured in Centimetres.)

Illustration 4 for 17Find_the_volume_of_the_below_ …

(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

Answers and Explanations

Answer 1 (A)

  • 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

Answer 1 (B)

  • A cuboid having a dimension is
  • Means its

Answer 2 (A)

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

  • Therefore, the surface area of cylinder is .

Answer (3)

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

Answer 4 (A)

  • A cube of side length (a)

  • Therefore, the volume of cube is .

Answer 4 (B)

  • A cuboid having a dimension is
  • Means its

  • Therefore, the volume of cuboid is .

Answer 4 (C)

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

  • Therefore, the volume of cylinder is .

Answer 5 (A)

  • Surface area of cube is .
  • If side of a cube is β€œa” than,

  • So , side of a cube is 7 cm

Answer 5 (B)

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

Answer 6 (A)

  • Curved area surface of cylinder
  • Radius of Cylinder (r)

  • Where β€œh” is height of cylinder.

  • So, height of Cylinder is 6 cm.

Answer 6 (B)

  • Height of cylinder
  • Radius of cylinder

Answer 7 (A)

  • Length of Cuboid (l)
  • Breadth of cuboid (b)
  • Suppose Height of Cuboid

  • So height of Cuboid is 5 cm.

Answer 7 (B)

  • Length of Cuboid (l)
  • Breadth of cuboid (b)
  • Height of Cuboid (h)

Answer 8 (A)

  • 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:

Answer 9 (A)

  • 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:

Answer 10 (A)

  • 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

Answer 11 (A)

  • 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

Answer (12)

  • 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

Answer (13)

  • 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

Answer (14)

  • 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)
  • Breadth (b)
  • 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.
Illustration 5 for Answers_and_Explanations

Answer (15)

  • Swimming pool is of a cuboid shape having length (l)
  • Breadth
  • 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.
Illustration 6 for Answers_and_Explanations
  • So, while we calculate the surface area we consider only 5 side.

  • Now,

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

Answer (16)

  • Volume of the prism

  • Hence , the Volume of the given prism is

Answer (17)

  • 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

Answer 18 (A)

  • 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)
  • Breadth (b)
  • And height (h)
  • So,

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

  • Now, Surface area of wooden box

  • So, Surface area of Wooden box is

Answer 19 (A)

  • Volume of wooden box

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

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

  • So, Volume of wooden box

  • So, Volume of Wooden box is

Answer 20 (A)

  • 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,

Answer 21 (A)

  • Surface area of the pipe

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

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

  • Side Circle Surface area:

  • Now,

  • So, Surface area of pipe

Answer (22)

  • 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 β€œ4” complete disc formed after recasting

Answer 23 (A)

  • Volume of the Solid formed

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

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

  • Now,

Answer 24 (A)

  • Surface Area of Solid formed

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

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

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

  • Surface Area of Solid formed

Answer (25)

  • A rectangular Sheet Dimension
  • So, its Length
  • And breadth
  • 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

Answer 26 (A)

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

Answer 26 (B)

  • The area covered by roller in one revolution is equal to the Cylindrical Surface Area of Roller.

  • So, in revolution Roller cover area.

Answer 26 (C)

  • Area covered by the roller in 250 revolutions.

  • So, 250 revolution roller cover

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