Class 9 Maths: Surface Area and Volumes – Extra Questions with Answers
Q. 1 A rectangular prism-shaped swimming pool has a length of 15 meters and a width of 8 meters. If the pool is filled to a depth of 2.2 meters, what is the volume of water in the pool in cubic meters?
Check Solution
Ans: C
Solution:
Volume = Length × Width × Depth = 15 m × 8 m × 2.2 m = 264 cubic meters
Answer: 264
Q. 2 A cylindrical water tank is 3.5 meters in diameter and 5 meters deep. Calculate the cost of painting the inner curved surface of the tank at a rate of Rs 12 per square meter.
Check Solution
Ans: C
Solution:
Radius (r) = 3.5/2 = 1.75 m
Height (h) = 5 m
Curved surface area = 2 * π * r * h = 2 * (22/7) * 1.75 * 5 = 55 sq m
Cost = 55 * 12 = Rs 660
Answer: 660
Q. 3 If the lateral surface area of a cylinder is 125.6 $cm^2$ and its radius is 4 cm, then find its height.
Check Solution
Ans: C
Solution:
Lateral surface area of a cylinder = $2\pi rh$
$125.6 = 2 \times 3.14 \times 4 \times h$
$h = 125.6 / (2 \times 3.14 \times 4)$
$h = 125.6 / 25.12$
$h = 5$
Answer: 5 cm
Q. 4 The volume of a cube is $64 cm^3$. What is its total surface area?
Check Solution
Ans: B
Solution:
Let s be the side length of the cube. The volume of a cube is $s^3$.
$s^3 = 64 cm^3$
$s = \sqrt[3]{64} = 4 cm$
The surface area of a cube is $6s^2$.
$6s^2 = 6(4^2) = 6(16) = 96 cm^2$
Answer: 96 cm^2
Q. 5 How many lead balls, each with a diameter of 2 cm, can be made from a sphere of radius 10 cm?
Check Solution
Ans: B
Solution:
Volume of large sphere: (4/3)π(10^3) = (4000/3)π cm^3
Volume of each small lead ball: (4/3)π(1^3) = (4/3)π cm^3
Number of lead balls = (4000/3)π / (4/3)π = 1000
Answer: 1000
Q. 6 A spherical water tank has a radius of 3 meters. How many smaller spherical tanks, each with a radius of 1 meter, can be filled using the water from the larger tank?
Check Solution
Ans: D
Solution:
Volume of large tank = (4/3)π(3^3) = 36π cubic meters
Volume of small tank = (4/3)π(1^3) = (4/3)π cubic meters
Number of small tanks = (36π) / ((4/3)π) = 27
Answer: 27
Q. 7 A solid metallic sphere has a diameter of 21 cm. It is melted and recast into a hemispherical bowl. The cost of polishing the outer surface of the bowl is Rs 25 per $100 cm^2$. Find the total cost of polishing the bowl.
Check Solution
Ans: C
Solution:
Sphere radius, r = 21/2 cm.
Sphere volume = (4/3)πr³ = (4/3)π(21/2)³ cm³
Hemisphere radius, R:
Volume of hemisphere = (1/2)(4/3)πR³ = (4/3)π(21/2)³
R³ = 2*(21/2)³
R = 21 cm
Surface area to be polished = 2πR² = 2π(21)² = 2772 cm²
Cost = (2772/100) * 25 = Rs 693
Answer: Rs 693
Q. 8 A rectangular storage container has dimensions of 210 m, 105 m, and 17 m. If each carton requires 357 $m^3$ of space, how many cartons can be stored in the container?
Check Solution
Ans: C
Solution:
Volume of container = 210 * 105 * 17 = 374850 $m^3$
Number of cartons = 374850 / 357 = 1050
Answer: 1050
Q. 9 How many spheres, each with a radius of 3 cm, can be made from a solid metallic cylinder with a radius of 4 cm and a height of 45 cm, assuming no material is lost in the process?
Check Solution
Ans: A
Solution:
1. Calculate the volume of the cylinder: V_cylinder = π * r_cylinder² * h_cylinder = π * 4² * 45 = 720π cm³
2. Calculate the volume of one sphere: V_sphere = (4/3) * π * r_sphere³ = (4/3) * π * 3³ = 36π cm³
3. Divide the cylinder’s volume by the sphere’s volume: Number of spheres = V_cylinder / V_sphere = 720π / 36π = 20
Answer: 20
Q. 10 A circus tent is cylindrical to a height of 4 metres and conical above it. The tent’s diameter is 100 m and the slant height of the conical portion is 52 m. Calculate the length of the canvas, which is 4 m wide, needed to make the tent.
Check Solution
Ans: C
Solution:
Radius (r) = 100/2 = 50 m
Curved Surface Area of cylinder = 2πrh = 2 * π * 50 * 4 = 400π m²
Curved Surface Area of cone = πrl = π * 50 * 52 = 2600π m²
Total surface area = 400π + 2600π = 3000π m²
Length of canvas = Total surface area / Width = 3000π / 4 = 750π m ≈ 750 * 22/7 m ≈ 2357.14 m
Answer: 2357.14
Next Topic: Statistics
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