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CBSE Class 9  >  Class 9 Test  >  Mathematics (Maths)   >  Test: Surface Area Sphere and Hemisphere - Class 9 MCQ

Surface Area Sphere and Hemisphere - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Surface Area Sphere and Hemisphere (10 Questions)

You can prepare effectively for Class 9 Mathematics (Maths) Class 9 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Surface Area Sphere and Hemisphere". These 10 questions have been designed by the experts with the latest curriculum of Class 9 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Surface Area Sphere and Hemisphere - Question 1
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A sphere has a surface area of 301.84 cm2. Its diameter is​

Detailed Solution: Question 1

Formula for the surface area of a sphere:

Surface Area = 4πr²

Where:

  • r is the radius,
  • π = 3.1416.

301.84 = 12.5664 × r²
r² = 301.84 / 12.5664
r² = 24
r = √24 = 4.9 cm

The diameter of the sphere is:

Diameter = 2 × r = 2 × 4.9 = 9.8 cm

Test: Surface Area Sphere and Hemisphere - Question 2
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A hemispherical bowl is made of steel, 1 cm thick. The inner radius of the bowl is 6 cm. The outer curved surface area of the bowl is​

Detailed Solution: Question 2

The inner radius of the hemispherical bowl is 6 cm, and the thickness is 1 cm. The outer radius is:

R = 6 + 1 = 7 cm.

The formula for the curved surface area (CSA) of a hemisphere is:

CSA = 2πR²

Solution:

Substitute R = 7 cm into the formula:

CSA = 2π(7²) = 2π(49) = 98π

Take π = 3.14:

CSA = 98 × 3.14 = 307.72 cm²

Final Answer:

Rounding off, the outer curved surface area is approximately:

(c) 308 cm².

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Test: Surface Area Sphere and Hemisphere - Question 3
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The total surface area of a hemispherical bowl of radius 77 cm is​

Detailed Solution: Question 3

The total surface area of a hemispherical bowl can be calculated using the formula:

  • Total Surface Area = 3πr²

Where:

  • r is the radius of the hemisphere.

For a hemispherical bowl with a radius of 77 cm:

  • Substituting the value into the formula:
  • Total Surface Area = 3 × π × (77)²
  • Total Surface Area = 3 × π × 5929
  • Total Surface Area ≈ 3 × 18606.5
  • Total Surface Area ≈ 55819.5 cm²

Rounding this value gives us approximately 55902 cm².

Test: Surface Area Sphere and Hemisphere - Question 4
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If the radius of a sphere is tripled, the ratio of the surface area of original sphere to that of the second is

Detailed Solution: Question 4

The surface area of a sphere is given by:

Surface Area = 4πr²

Let the radius of the original sphere be r₁ = r and the radius of the second sphere be r₂ = 3r (radius is tripled).

  1. Surface Area of the Original Sphere: S₁ = 4πr²

  2. Surface Area of the Second Sphere: S₂ = 4π(3r)² = 4π × 9r² = 36πr²

  3. Ratio of Surface Areas:

S₁ / S₂ = (4πr²) / (36πr²) = 1 / 9

The ratio of the surface area of the original sphere to the second is: 1 : 9

Test: Surface Area Sphere and Hemisphere - Question 5
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A hemispherical bowl has total surface area 96 cm2. The lateral surface area of 5 such bowls is​

Detailed Solution: Question 5

Using π = 22/7, let's recalculate.

The total surface area (TSA) of a hemispherical bowl is the sum of the lateral surface area (LSA) and the area of the circular base:

TSA = LSA + Area of Base

We are given:

TSA = 96 cm²

Using the formula:

TSA = 3πr²

Substitute π = 22/7:

TSA = 3 × 22/7 × r²

Simplify:

96 = 3 × 22/7 × r²

96 × 7 = 66 × r²
672 = 66 × r²

Now calculate the lateral surface area (LSA) of one hemisphere:

LSA = 2πr² / 2

Simplify:

LSA = 44 × r²

Now, solve for r²:

r² = 672 / 66 = 10.18 cm²

For 5 such bowls:

Total LSA = 5 × 64 = 320 cm²

Test: Surface Area Sphere and Hemisphere - Question 6
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The lateral surface area of a hemisphere whose total surface area is 525 cm2 is​

Detailed Solution: Question 6

The total surface area (TSA) of a hemisphere is given by:

TSA = LSA + Area of Base

Where:

  • LSA = 2πr² (lateral surface area),
  • Area of Base = πr².

Thus:

TSA = 2πr² + πr² = 3πr²

Given TSA = 525 cm², and using π = 22/7:

3πr² = 525

Substitute π = 22/7:

3 × 22/7 × r² = 525

Simplify:

66/7 × r² = 525

r² = (525 × 7) / 66 = 3675 / 66 = 55.68 cm²

Now calculate the lateral surface area (LSA):

LSA = 2πr²

Simplify:

LSA = 2 × 22/7 × 55.68 = 44 × 55.68 / 7 = 2449.92 / 7 ≈ 350 cm²

Test: Surface Area Sphere and Hemisphere - Question 7
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The surface area of a sphere of radius 7 cm is​

Detailed Solution: Question 7

The surface area of a sphere is calculated using the formula:

Surface Area = 4πr²

Where:

  • r = 7 cm (radius of the sphere),
  • π = 3.1416.

Substitute the values into the formula:

Surface Area = 4 × 3.1416 × 7²

Step-by-step calculations:

  1. 7² = 49
  2. 4 × 3.1416 × 49 = 4 × 153.9384 = 615.7536 cm²

Approximating, the surface area is: 616 cm²

Test: Surface Area Sphere and Hemisphere - Question 8
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The total surface area of a hemispherical bowl of diameter 28 cm is​

Detailed Solution: Question 8

The total surface area of a hemispherical bowl is calculated using the formula:

Total Surface Area = 3πr²

Where:

  • r is the radius of the hemisphere,
  • π = 3.1416.

Given the diameter = 28 cm, the radius r = 28 / 2 = 14 cm.

Substituting into the formula:

Total Surface Area = 3 × 3.1416 × 14²

Step-by-step calculations:

  1. 14² = 196
  2. Total Surface Area = 3 × 3.1416 × 196 = 3 × 615.751 = 1847.253 cm²

Approximating, the total surface area is: 1848 cm²

Test: Surface Area Sphere and Hemisphere - Question 9
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The diameter of one sphere is 21 cm, and the diameter of another sphere is 14 cm, the ratios of their curved surface areas is

Detailed Solution: Question 9

The formula for the curved surface area of a sphere is:

Curved Surface Area = 4πr²

For two spheres, the ratio of their curved surface areas depends on the square of their radii:

Ratio of curved surface areas = r₁² / r₂²

  1. The radius of the first sphere (r₁) is:

    r₁ = Diameter / 2 = 21 / 2 = 10.5 cm

  2. The radius of the second sphere (r₂) is:

    r₂ = Diameter / 2 = 14 / 2 = 7 cm

  3. The ratio of their curved surface areas is:

    r₁² / r₂² = (10.5)² / (7)² = 110.25 / 49 = 9 / 4

The ratio of their curved surface areas is 9 : 4.

Test: Surface Area Sphere and Hemisphere - Question 10
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The curved surface area of a hemisphere of diameter 28 cm is​

Detailed Solution: Question 10

The curved surface area of a hemisphere is calculated using the formula:

Curved Surface Area = 2πr²

Given the diameter d = 28 cm, the radius r = 28 / 2 = 14 cm.

Substitute into the formula:

Curved Surface Area = 2 × 3.1416 × 14²

14² = 196

Curved Surface Area = 2 × 3.1416 × 196 = 2 × 615.75104 = 1231.502 cm²

Approximating, the curved surface area is: 1232 cm²

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About this Class 9 Practice Test

This test contains 10 MCQs on Surface Area Sphere and Hemisphere with detailed solutions for each question. It is part of the Mathematics (Maths) Class 9 course on EduRev, designed to align with the current Class 9 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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