Calculate the volume of a sphere with radius 7 cm (Take pi = 2... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

Back to Practice Questions

MathematicsMathematics

Prev Next

Calculate the volume of a sphere with radius 7 cm (Take pi = 22/7).

1437.33 cm³

1500 cm³

1200 cm³

1600 cm³

Correct Answer

📐 MA • Math Direct FormulaMathematicsMathematics

Option A

1437.33 cm³

Quick Summary:

Since the formula involves $r^{3} = 7^{3} = 343$ , and we multiply by $\frac{22}{7}$ , notice that $343 / 7 = 49$ . The calculation simplifies to $4 \times 22 \times 49 / 3 = 88 \times 49 / 3 = 4312 / 3$ . Dividing $4312$ by $3$ gives approximately $1437.33$ .

🎯

Crack Mathematics with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

Radius of the sphere r = 7 cm, value of pi = 22/7.

🔢 Formula Used

V=43πr3V = \frac{4}{3} \pi r^{3}V=34​πr3

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often confuse the surface area formula $4 \pi r^{2}$ with the volume formula $\frac{4}{3} \pi r^{3}$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the formula

The volume of a sphere is given by the standard geometric formula involving the radius $r$ .

V=43πr3V = \frac{4}{3} \pi r^{3}V=34​πr3

Substitute the values

Substitute $r = 7$ and $\pi = 22/7$ into the volume equation.

V=43×227×73V = \frac{4}{3} \times \frac{22}{7} \times 7^{3}V=34​×722​×73

Simplify and Calculate

Cancel one $7$ from the numerator and denominator, leaving $4 \times 22 \times 7^{2} / 3$ .

V=4×22×493=43123V = \frac{4 \times 22 \times 49}{3} = \frac{4312}{3}V=34×22×49​=34312​

Final Division

Divide $4312$ by $3$ to obtain the final volume in cubic centimeters.

V≈1437.33 cm3V \approx 1437.33 \text{ cm}^{3}V≈1437.33 cm3

✅

A is correct because the calculation of $\frac{4}{3} \times \frac{22}{7} \times 7^{3}$ results in exactly $1437.33 \text{ cm}^{3}$ .

Core Concepts Used

Click any tag to open in AI Tutor

Mensuration of 3D solids Volume of a sphere Algebraic substitution

💡 EXAM TIP

Understanding volume formulas is essential for calculus problems involving rates of change, specifically related rates where volume changes with respect to time.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)