We are asked how the volume of the given cylinder would change if the height was tripled.
Therefore, the radius of the bigger cylinder is r= 5 cm and the height is h= 24 cm. Now, let's find the volume of this cone.
\begin{gathered}
V_\text{big}=\pi ({\color{#0000FF}{5}})^2({\color{#009600}{24}})=600\pi
\end{gathered}
Since the ratio between the volume of the big cylinder and the old cylinder is 600Ď€/200Ď€=3, the volume of the cylinder triples if we triple its height.
b As in Part A, we are given a cylinder with a radius of 5 cm and a height of 8 cm. From Part A we know that the volume of the given solid is V_\text{cylinder}=200\pi cubic centimeters. We are asked to find how the volume of the given cylinder would change if the radius of the base was tripled.
Therefore, the radius of the bigger cylinder is r= 15 cm and the height is h= 8 cm. Now, let's find the volume of this cylinder.
\begin{gathered}
V_\text{big}=\pi ({\color{#0000FF}{15}})^2({\color{#009600}{8}})=1800\pi
\end{gathered}
Since the ratio between the volume of the big cylinder and the old cylinder is 1800Ď€/200Ď€=9, the volume of the cylinder is 9 times larger if we triple its radius.
c As in Part A, we are given a cylinder with a radius of 5 cm and a height of 8 cm. From Part A we know that the volume of the given solid is V_\text{cylinder}=200\pi cubic centimeters. We are asked to find how the volume of the given cylinder would change if the radius and the height were tripled.
Therefore, the radius of the bigger cylinder is r= 15 cm and the height is h= 24 cm. Now, let's find the volume of this cylinder.
\begin{gathered}
V_\text{big}=\pi ({\color{#0000FF}{15}})^2({\color{#009600}{24}})=5400\pi
\end{gathered}
Since the ratio between the volume of the big cylinder and the old cylinder is 5400Ď€/200Ď€=27, the volume of the cylinder is 27 times larger if we triple its radius and height.
d As in Part A, we are given a cylinder with a radius of 5 cm and a height of 8 cm. From Part A we know that the volume of the given solid is V_\text{cylinder}=200\pi cubic centimeters. We are asked to find how the volume of the given cylinder would change if its dimensions were exchanged.
Therefore, the radius of the bigger cylinder is r= 8 cm and the height is h= 5 cm. Now, let's find the volume of this cylinder.
\begin{gathered}
V_\text{big}=\pi ({\color{#0000FF}{8}})^2({\color{#009600}{5}})=320\pi
\end{gathered}
Since the ratio between the volume of the big cylinder and the old cylinder is 320Ď€/200Ď€=1.6, the volume of the cylinder is 1.6 times larger if we exchange its dimensions.
