[tex]\large\underline{\sf{Solution-}}[/tex]
Given that, height of cylinder exceeds the radius by 7 cm
Let assume that
Radius of cylinder = r cm
Height of cylinder = h = r + 7
According to statement, it is further given that the curved surface area of a cylinder is three times the base area.
We know,
Curved Surface Area of cylinder of radius r and height h is given by
[tex]\boxed{ \rm{ \:CSA_{(Cylinder)} \: = \: 2 \: \pi \: r \: h \: \: }} \\ [/tex]
and
[tex]\boxed{ \rm{ \:Base \: Area_{(Cylinder)} \: = \: \pi \: {r}^{2} \: \: }} \\ [/tex]
So,
[tex]\rm \: 2\pi \: rh \: = \: 3\pi {r}^{2} \\ [/tex]
[tex]\rm \: 2h \: = \: 3r \\ [/tex]
On substituting the value of h, we get
[tex]\rm \: 2 \:(r + 7) \: = \: 3r\\ [/tex]
[tex]\rm \: 2r + 14 \: = \: 3r\\ [/tex]
[tex]\rm \: 3r - 2r = 14\\ [/tex]
[tex]\rm\implies \:r \: = \: 14 \: cm \\ [/tex]
So, we have
Radius of cylinder, r = 14 cm
Height of cylinder, h = r + 7 = 14 + 7 = 21 cm
Now,
[tex]\rm \: Volume _{(Cylinder)} \: = \: \pi \: {r}^{2} \: h \\ [/tex]
[tex]\rm \: = \:\dfrac{22}{7} \times 14 \times 14 \times 21 \\ [/tex]
[tex]\rm \: = \:22 \times 2 \times 14 \times 21 \\ [/tex]
[tex]\rm \: = \:12936 \: {cm}^{3} \\ [/tex]
Hence,
[tex]\color{green}\rm\implies \:\boxed{ \rm{ \:Volume _{(Cylinder)} = 12936 \: {cm}^{3} \: }} \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]