Which expression represents the volume, in cubic units, of the composite figure? pi(5^2)(13)-1/3pi(5^2)(12) pi(5^2)(13)-1/3pi(5^2)(25) pi(5^2)(13)+1/3pi(5^2)(12) pi(5^2)(13+1/3p…

Question

asked Sep 12, 2021 53.2k views

2 Answers

Silverdagger · Answer 1 · 2021-09-16T19:38:17+0000

Answer:

C.

$V = \pi * 5^2(13) +(1)/(3)\pi * 5^2 (12)$

Explanation:

Given:

The figure is a combination of a cone and a cylinder

Radius (of both),
r = 5

Height of Cylinder,
H_1 = 13

Height of Cone,
H_2 = 25 - 13 = 12

Required:

Volume of the figure

Let V represents the volume of the figure;

V_1 represents the volume of the cylinder

V_2 represents the volume of the cone

So,
V = V_1 + V_2

Where
$V_1 = \pi r^2H_1$ and
$V_2 = (1)/(3)\pi r^2 H_2$

So, V becomes

$V = \pi r^2H_1 + (1)/(3)\pi r^2 H_2$

Factorize the above expression

$V = \pi r^2(H_1 + (1)/(3)H_2)$

Substitute
r = 5 ;
H_1 = 13 ;
H_2 = 12

$V = \pi * 5^2(13 + (1)/(3) * 12)$

Open Bracket

$V = \pi * 5^2(13) +\pi * 5^2 (1)/(3) (12)$

Reorder

$V = \pi * 5^2(13) +(1)/(3)\pi * 5^2 (12)$

From the list of options given, option c is correct.