Photo AI

A sphere has a radius of 3 cm - OCR - GCSE Maths - Question 19 - 2023 - Paper 2

Question icon

Question 19

A-sphere-has-a-radius-of-3-cm-OCR-GCSE Maths-Question 19-2023-Paper 2.png

A sphere has a radius of 3 cm. Calculate the volume of the sphere. Give your answer in terms of $ p$ in its simplest form. [The volume $V$ of a sphere with radius $... show full transcript

Worked Solution & Example Answer:A sphere has a radius of 3 cm - OCR - GCSE Maths - Question 19 - 2023 - Paper 2

Step 1

Calculate the volume of the sphere

96%

114 rated

Tired rob

Only available for registered users.

Sign up now to view full answer, or log in if you already have an account!

Answer

To find the volume VV of a sphere, we use the formula: V=43Ï€r3V = \frac{4}{3} \pi r^3

Given that the radius rr is 3 cm, we substitute: V=43Ï€(3)3V = \frac{4}{3} \pi (3)^3

Calculating the radius cubed: (3)3=27(3)^3 = 27

Now substituting back into the formula: V=43π⋅27V = \frac{4}{3} \pi \cdot 27

Simplifying, we have: V=1083Ï€=36Ï€V = \frac{108}{3} \pi = 36\pi

Thus, the volume of the sphere is: V=36Ï€ cm3V = 36\pi \text{ cm}^3

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

Other GCSE Maths topics to explore

Number Toolkit

Maths - Edexcel

Prime Factors, HCF & LCM

Maths - Edexcel

Powers, Roots & Standard Form

Maths - Edexcel

Simple & Compound Interest, Growth & Decay

Maths - Edexcel

Fractions, Decimals & Percentages

Maths - Edexcel

Rounding, Estimation & Bounds

Maths - Edexcel

Surds

Maths - Edexcel

Algebraic Roots & Indices

Maths - Edexcel

Expanding Brackets

Maths - Edexcel

Factorising

Maths - Edexcel

Completing the Square

Maths - Edexcel

Algebraic Fractions

Maths - Edexcel

Rearranging Formulae

Maths - Edexcel

Algebraic Proof

Maths - Edexcel

Linear Equations

Maths - Edexcel

Solving Quadratic Equations

Maths - Edexcel

Simultaneous Equations

Maths - Edexcel

Iteration

Maths - Edexcel

Forming & Solving Equations

Maths - Edexcel

Functions

Maths - Edexcel

Coordinate Geometry

Maths - Edexcel

Estimating Gradients & Areas under Graphs

Maths - Edexcel

Real-Life Graphs

Maths - Edexcel

Transformations of Graphs

Maths - Edexcel

Sequences

Maths - Edexcel

Direct & Inverse Proportion

Maths - Edexcel

Standard & Compound Units

Maths - Edexcel

Exchange Rates & Best Buys

Maths - Edexcel

Geometry Toolkit

Maths - Edexcel

Angles in Polygons & Parallel Lines

Maths - Edexcel

Bearings, Scale Drawing, Constructions & Loci

Maths - Edexcel

Area & Perimeter

Maths - Edexcel

Right-Angled Triangles - Pythagoras & Trigonometry

Maths - Edexcel

Sine, Cosine Rule & Area of Triangles

Maths - Edexcel

Vectors

Maths - Edexcel

Transformations

Maths - Edexcel

Scatter Graphs & Correlation

Maths - Edexcel

Statistics

Maths - Edexcel

Ratio Analysis and Problem Solving

Maths - Edexcel

Inequalities

Maths - Edexcel

Volume, Area & Surface Area

Maths - Edexcel

The Circle

Maths - Edexcel

Probability

Maths - Edexcel

Trigonometry

Maths - Edexcel

Growth & Decay

Maths - Edexcel

Outliers

Maths - Edexcel

;