MATHEMATICS

JAMB 2019 - Question 5

Mathematics 2019 JAMB Past Questions - Question 5: A student blows a balloon and its volume increases at a rate of π(20-t2)cm3 s-1 after t seconds. If the initial volume is 0cm3, find the volume of the balloon after 2 seconds.

A student blows a balloon and its volume increases at a rate of π(20-t2)cm3 s-1 after t seconds. If the initial volume is 0cm3, find the volume of the balloon after 2 seconds.
A:
B:
C:
D:
Examkits App

Examkit's JAMB CBT App

Practice JAMB offline with our Online, PC and Mobile App

  • ✅ 25+ years of past questions (2000 to 2025)
  • ✅ Video solutions and explanation to questions
  • ✅ E-library
  • ✅ Study by topic
  • ✅ And more.

Correct Answer

B

Explanation

To find the volume of the balloon after 2 seconds, we can integrate the given rate of change of volume with respect to time.The rate of change of volume is given as π(20 - t^2) cm^3 s^-1. To find the volume after 2 seconds, we integrate this expression with respect to t from 0 to 2:∫[0 to 2] π(20 - t^2) dtThis integration will give us the total change in volume from t = 0 to t = 2 seconds.Evaluating the integral:∫[0 to 2] π(20 - t^2) dt = π[20t - (t^3)/3] evaluated from 0 to 2                          = π[40 - (8/3)]                          = π(120/3 - 8/3)                          = π(112/3)                          = 112π/3 cm^3So, the volume of the balloon after 2 seconds is 112π/3 cm^3.To find the volume of the balloon after 2 seconds, we can integrate the given rate of change of volume with respect to time.The rate of change of volume is given as π(20 - t^2) cm^3 s^-1. To find the volume after 2 seconds, we integrate the rate of change of volume with respect to time from 0 to 2 seconds:∫[0 to 2] π(20 - t^2) dtEvaluating this integral gives us the change in volume over the interval [0, 2]. Adding this change to the initial volume of 0 cm^3 gives us the volume of the balloon after 2 seconds.

Frequently Asked Questions

Examkits is a JAMB CBT practice platform that provides over 20 years of past questions, Post UTME questions, and detailed video solutions to help students prepare for their exams.

You can practice JAMB past questions online, on Android, or on a desktop using the Examkits app. Just register on our website and choose your preferred device.

Yes. Our Android and Windows versions support offline usage. Once downloaded and activated, no internet is required to use most of the features.

Yes, Examkits provides detailed video explanations for all JAMB past questions from 2000 to 2024, helping students understand how to solve each problem.

Examkits offers free practice for some subjects. However, full access requires a one-time affordable activation fee for each version of the app.