A Problem on Volume of a Cube/Geometrical Figure Cube

All the geometrical construction and geometrical figures like cube, cuboid, prism etc come under construction math and construction geometry where you will get more information about these geometrical figures and there attributes.

Topic : Volume of a cube

A Cube is a Geometrical Figure with dimension of equal sides, here is one such example on Cube, to Find length of the side of cube, given volume of cube using indice laws.

Question : The volume of a cube is given by V = s³, where s is the length of a side. Find the length of a side of a cube if the volume is 700 in³.Round the answer to three decimal places.

Solution :

Given V = 700 in³

Also, volume of a cube is given by

V = s³

=> 700 = s³

=> s³ = 700

=> s = cuberoot(700)

=> s = 8.697

Length of a side of cube = 8.697 inches.

Word problem on Function and gas concentration as its dependencies

Functions are denoted as shown in the figure where there will be dependencies of one variable value to another.

Topic : Functions and variables values.

Variables, co-efficient are the terms found in functions.

Problem : The table lists future concentrations of a certain green house gas in parts per billion (ppb), If current trends continue.

a) Let x = 0 correspond to 2010 and x = 20 correspond to 2030. Find C and a so that f(x) = Ca^x models the data.

b) Estimate the gas concentration in 2021.

Year ------ Gas(ppb)
2010 ------ 0.74 (when x = 0)
2015 ------ 0.86
2020 ------ 0.99
2025 ------ 1.15
2030 ------ 1.34 (when x = 20)

Solution :

a) We have function ,
f(x) = Ca^x

x = 0 ; f(0) = Ca⁰ = C*1 = C

So f(0) = 0.74 ; C = 0.74

and x = 20 ; f(x) = C a²⁰ = 0.74 a²⁰

f(20) = 1.34 (from the table)

So 1.34 = 0.74 a²⁰ ; a²⁰ = 1.34/0.74 = 1.8108

So a = 1.0301


b) To find gas concentration at the year 2021, we have to find f(21)

f(21) = Ca²¹ = 0.74 (1.0301)²¹

= 0.74 * 1.8641

= 1.37943

So f(21) approximately 1.38

Therefore gas concentration at 2021 will be 1.38

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