Home / Class 10 Math / Ch 13 Surface Area and Volumes- MCQ Online Test 1 Class 10 Maths
Chapter 13 Surface Area and Volumes- MCQ Online Test 1 Class 10 Maths
1.If the volume of a cube is 1728, the length of its edge is equal to 20 cm 19 cm 12 cm 15 cm
2. Two cubes each of 10 cm edge are joined end to end. The surface area of the resulting cuboid is 1700 cm2 1400 cm2 1000 cm2 4000 cm2
3. A rectangular sheet of paper 44 cm × 18 cm is rolled along its length and a cylinder is formed. The volume of the cylinder so formed is equal to (Take π = 22/7) 2700 cm3 2799 cm3 2772 cm3 3272 cm3
4. If the radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 , then its radius is equal to (Take π = 22/7) 14 cm 12 cm 10 cm 6 cm
5. If the curved surface area of a solid right circular cylinder of height h and radius r is one-third of its total surface area, then h = 2 r h = 1/4 r h = 1/2 r h = 3/2 r
6. A hollow cylindrical pipe is 21 cm long. If its outer and inner diameters are 10 cm and 6 cm respectively, then the volume of the metal used in making the pipe is (Take π = 22/7) 1056 cm3 1060 cm3 1013 cm3 1056 cm3
7. If the radius and slant height of a cone are in the ratio 4 : 7 and its curved surface area is 792 , then its radius is (Take π = 22/7) 15 cm 12 cm 17 cm 19 cm
8. If the radius of the base and the height of a right circular cone are respectively 21 cm and 28 cm, then the curved surface area of the cone is (Take π = 22/7) 2350 cm2 2210 cm2 3310 cm2 2310 cm2
9. A conical tent with base-radius 7 m and height 24 m is made from 5 m wide canvas. The length of the canvas used is (Take π = 22/7) 150 m 110 m 100 m 120 m
10. The total surface area of a solid hemisphere of radius 3.5 m is covered with canvas at the rate of Rs. 20 per. The total cost to cover the hemisphere is (Take π = 22.7) Rs. 2300 Rs. 2460 Rs. 2310 Rs. 2450
Class 10 Surface Area and Volumes Quiz 1
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Question 1 of 10
1. Question
If the volume of a cube is 1728 cm3 , the length of its edge is equal to
Correct
Given, volume of cube = 1728cm3
Let l be the side of the cube
∴ volume of the cube =l3
∴ l3 = 1728cm3
∴ l = 12 cm
Incorrect
Given, volume of cube = 1728cm3
Let l be the side of the cube
∴ volume of the cube =l3
∴ l3 = 1728cm3
∴ l = 12 cm
Question 2 of 10
2. Question
Two cubes each of 10 cm edge are joined end to end. The surface area of the resulting cuboid is
Correct
When edge of two cubes of 10 cm join together the dimensions of formed cuboid are
Length (l) = 20 cm
Breadth (b)=10 cm
Height (h)=10 cm
Total Surface Area Of cuboid = 2(lb+bh+hl)
= 2(20×10 + 10×10 + 10×20)
= 2(200+100+200)
= 2(500)
= 1000 cm²
Incorrect
When edge of two cubes of 10 cm join together the dimensions of formed cuboid are
Length (l) = 20 cm
Breadth (b)=10 cm
Height (h)=10 cm
Total Surface Area Of cuboid = 2(lb+bh+hl)
= 2(20×10 + 10×10 + 10×20)
= 2(200+100+200)
= 2(500)
= 1000 cm²
Question 3 of 10
3. Question
A rectangular sheet of paper 44 cm × 18 cm is rolled along its length and a cylinder is formed. The volume of the cylinder so formed is equal to (Take π = 22/7)
Correct
Length of the sheet = circumference of cylinder base
2×π×r = 44cm
2 × 22/7 × r = 44 cm
r = (44×7)/(2×22)
r = 7cm
Therefore, radius of the cylinder = r = 7cm
Height of the cylinder = Breadth of the rectangle
h = 18cm
Volume of the cylinder = π×r2×h
=22/7 × 7 × 7 × 18
=22 × 7 × 18
=2772cm3
Incorrect
Length of the sheet = circumference of cylinder base
2×π×r = 44cm
2 × 22/7 × r = 44 cm
r = (44×7)/(2×22)
r = 7cm
Therefore, radius of the cylinder = r = 7cm
Height of the cylinder = Breadth of the rectangle
h = 18cm
Volume of the cylinder = π×r2×h
=22/7 × 7 × 7 × 18
=22 × 7 × 18
=2772cm3
Question 4 of 10
4. Question
If the radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm3, then its radius is equal to (Take π = 22/7)
Correct
Given, volume of a cylinder =πr2h=550 cm3
Also, given, r/h = 5/7
∴h= 7r/5
Given, πr2h=550
Thus, the radius of the cylinder is 5 cm.
Incorrect
Given, volume of a cylinder =πr2h=550 cm3
Also, given, r/h = 5/7
∴h= 7r/5
Given, πr2h=550
Thus, the radius of the cylinder is 5 cm.
Question 5 of 10
5. Question
If the curved surface area of a solid right circular cylinder of height h and radius r is one-third of its total surface area, then
Correct
Curved surface area of cylinder = 2πrh square units
Total surface area of cylinder = 2πr(h+r) square units
Incorrect
Curved surface area of cylinder = 2πrh square units
Total surface area of cylinder = 2πr(h+r) square units
Question 6 of 10
6. Question
A hollow cylindrical pipe is 21 cm long. If its outer and inner diameters are 10 cm and 6 cm respectively, then the volume of the metal used in making the pipe is (Take π = 22/7)
Correct
Volume of cylinder = π(R²-r²)h
= π(5²-3²)×21
= π(25-9)×21
= π(16)×21
= 22/7 × 16 × 21
= 1056 cm³
Incorrect
Volume of cylinder = π(R²-r²)h
= π(5²-3²)×21
= π(25-9)×21
= π(16)×21
= 22/7 × 16 × 21
= 1056 cm³
Question 7 of 10
7. Question
If the radius and slant height of a cone are in the ratio 4 : 7 and its curved surface area is 792 , then its radius is (Take π = 22/7)
Correct
The ratio of the radius and height of the cone is 4 : 7.
Let the radius of the cone be 4x and the height be 7x
So,
Curved surface area of the cone = πrl
792 = 22/7 × 4x × 7x
x² = (792×7)/(22×4×7)
x² = 9
x = √9
x = 3 cm
So, the radius of the cone = 4 × 3 = 12 cm.
Incorrect
The ratio of the radius and height of the cone is 4 : 7.
Let the radius of the cone be 4x and the height be 7x
So,
Curved surface area of the cone = πrl
792 = 22/7 × 4x × 7x
x² = (792×7)/(22×4×7)
x² = 9
x = √9
x = 3 cm
So, the radius of the cone = 4 × 3 = 12 cm.
Question 8 of 10
8. Question
If the radius of the base and the height of a right circular cone are respectively 21 cm and 28 cm, then the curved surface area of the cone is (Take π = 22/7)
Correct
In a cone,
Slant height (l) =
⇒ l =
Curved surface area of a cone =πrl where, r is the radius of the cone and l is the slant height.
Hence, curved surface area of this cone = 22/7 × 21 × 35 = 2310cm2
Incorrect
In a cone,
Slant height (l) =
⇒ l =
Curved surface area of a cone =πrl where, r is the radius of the cone and l is the slant height.
Hence, curved surface area of this cone = 22/7 × 21 × 35 = 2310cm2
Question 9 of 10
9. Question
A conical tent with base-radius 7 m and height 24 m is made from 5 m wide canvas. The length of the canvas used is (Take π = 22/7)
Correct
Given, radius and height = 7m and 24m respectively
Slant height (l) =
⇒ l =
= √625 = 25cm
Also,
C.S.A=πrl
22/7 × 7 × 25 = 550 m2
Let x m of canvas is required of length 5 m,
Area of canvas = CSA
5x = 550 cm2
x= 110 m
Incorrect
Given, radius and height = 7m and 24m respectively
Slant height (l) =
⇒ l =
= √625 = 25cm
Also,
C.S.A=πrl
22/7 × 7 × 25 = 550 m2
Let x m of canvas is required of length 5 m,
Area of canvas = CSA
5x = 550 cm2
x= 110 m
Question 10 of 10
10. Question
The total surface area of a solid hemisphere of radius 3·5 m is covered with canvas at the rate of Rs. 20 per m2. The total cost to cover the hemisphere is (Take π = 22/7)
Correct
Total Surface Area of a hemisphere of radius ‘r’ =3πr2
Hence, total surface area of this hemisphere =3× 22/7 ×3.5×3.5=115.5 m2
∴ Cost of covering the hemisphere with canvas at the rate of Rs. 20 per m2=115.5×20 = Rs2310
Incorrect
Total Surface Area of a hemisphere of radius ‘r’ =3πr2
Hence, total surface area of this hemisphere =3× 22/7 ×3.5×3.5=115.5 m2
∴ Cost of covering the hemisphere with canvas at the rate of Rs. 20 per m2=115.5×20 = Rs2310
, then its radius is (Take π = 22/7)
