The volume of a sphere with radius r is 4/3πr³. Write a Python program to find the volume of spheres with radi

Exercises · Q18

Q. The volume of a sphere with radius r is 4/3πr³. Write a Python program to find the volume of spheres with radius 7cm, 12cm, 16cm, respectively.

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Concept understanding — Simple Interest Calculation

Simple Interest: The Cost of Borrowing (or the Reward for Saving)

Imagine you lend a friend ₹100. A year later, they return the ₹100. You're even — but you also missed the chance to use that ₹100 yourself for a whole year. That inconvenience has a price. In finance, that price is called interest.

Simple interest is the most straightforward way to calculate that price. It says: the interest you earn (or pay) each year is a fixed percentage of the original amount you started with — no matter how many years pass.

The Core Intuition

Think of it like renting money. If you rent a car for a day, you pay a fixed daily rate. If you rent it for 5 days, you pay 5 times that daily rate. Simple interest works the same way:

The Principal (P) is the amount you lend or borrow — the "car."
The Rate (R) is the daily rental charge, expressed as a percentage of the car's value — the "rent per day."
The Time (T) is how many days you keep the car — the number of years.

The total rent (interest) is just: daily rent × number of days.

The Precise Statement

\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}

Where:

P = Principal (the original sum of money)
R = Rate of interest per year (in percent)
T = Time period (in years)

The Total Amount (A) you get back (or owe) at the end is:

A = P + \text{SI}

Why Divide by 100?

The rate $R$ is given as a percentage — say 10%. "10% per year" means you get ₹10 for every ₹100 you lend, each year. So for a principal $P$ , the interest for one year is:

\frac{10}{100} \times P = 0.10 \times P

That's the same as $\frac{P \times R}{100}$ . For $T$ years, you multiply by $T$ , giving $\frac{P \times R \times T}{100}$ .

A Worked Example

You deposit ₹2000 in a bank that offers 8% simple interest per year. You leave it for 3 years.

P = ₹2000
R = 8
T = 3

\text{SI} = \frac{2000 \times 8 \times 3}{100} = \frac{48000}{100} = ₹480

So after 3 years, you earn ₹480 in interest. Your total amount becomes:

A = 2000 + 480 = ₹2480

Tip

Notice that each year you earn exactly the same interest: $\frac{2000 \times 8}{100} = ₹160$ . Year 1: ₹160, Year 2: another ₹160, Year 3: another ₹160. The interest never grows because it's always calculated on the original ₹2000, not on the growing balance.

The Key Property (and its Limitation)

Simple interest is linear — the interest grows at a constant rate each year. This makes it easy to calculate and understand. …

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Volume of a sphere = (4/3)πr³. Loop over the three radii using math.pi:

import math
for r in (7, 12, 16):
    volume = (4/3) * math.pi * r**3
    print("Radius:", r, "cm  Volume:", round(volume, 2), "cubic cm")

Expected output:

Radius: 7 cm  Volume: 1436.76 cubic cm
Radius: 12 cm  Volume: 7238.23 cubic cm …

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Compute volume = (4/3) * math.pi * r**3 for r = 7, 12, 16 — giving about 1436.76, 7238.23 and 17157.28 cubic cm respectively.

The concept is translating the formula V = 4/3 πr³ into Python: the exponent operator ** for r³, math.pi for an accurate π, and — crucially — writing the fraction as 4/3 (which in Python 3 is true division, 1.333…, not the 1 that integer division would give in some other languages).

# Volume of spheres of radius 7, 12 and 16 cm
import math

for r in (7, 12, 16):
    volume = (4/3) * math.pi * r**3
    print("Radius:", r, "cm  Volume:", round(volume, 2), "cubic cm")

Key lines:

r**3 — precedence: ** binds before *, so the cube is computed first, exactly as the formula wants.
math.pi (≈ 3.141592653589793) beats typing 3.14 — the book's own answers differ at the decimals if a truncated π is used.
The loop avoids writing the same formula three times.

Working, step by step:

r	r³	(4/3)·r³	× π → volume (rounded)
7	343	457.33…	1436.76 cm³
12	1728	2304	7238.23 cm³

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Q.The volume of a sphere with radius r is 4/3πr³. Write a Python program to find the volume of spheres with radius 7cm, 12cm, 16cm, respectively.

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