Question

a metallic right circular cylinder is 15 cm high and the diameter of its base is 14 cm. it is melted and recasted into another cylinder with radius 14 cm. find height,curved surface area and total surface area of the cylinder.​

Answer 1

Answer:

Answer is given below

Step-by-step explanation:

Height =15 cm

Diameter = 14 cm

radius =7cm

volume =

$\pi \times r ^{2} \times h = \frac{22}{7} \times 49 \times 15 {cm}^{3} \\ = 22 \times 7 \times 15 {cm}^{3}$

radius of the new cylinder =14 cm

let the height be h

volume =

$\pi \times {r}^{2} \times h$

$= > 770 = \frac{22}{7} \times 14 \times 14 \times h \\ = > 770 = 22 \times 2 \times 14 \times h$

$= > h = 770 \div 22 \times 2 \times 14 \\ = > h = \frac{5}{14} \\ = > h = 3.5cm$

height =3.5 cm

CSA =

$2 \times \pi \times r \times h \\ = 2 \times \frac{22}{7} \times 14 \times 3.5 {cm}^{2} \\ = 308 {cm}^{2}$

TSA =

$2 \times \pi \times r(h + r) \\ = 2 \times \frac{22}{7} \times 14 \times (3.5 + 14) {cm}^{2} \\ = 88 \times 17.5 {cm}^{2} \\ = 1540 {cm}^{2}$

Answer 2

Answer:

Height =15 cm

Diameter = 14 cm

radius =7cm

volume =

\begin{gathered}\pi \times r ^{2} \times h = \frac{22}{7} \times 49 \times 15 {cm}^{3} \\ = 22 \times 7 \times 15 {cm}^{3} \end{gathered}

π×r

2

×h=

7

22

×49×15cm

3

=22×7×15cm

3

radius of the new cylinder =14 cm

let the height be h

volume =

\begin{gathered}\pi \times {r}^{2} \times h \\ \end{gathered}

π×r

2

×h

\begin{gathered} = > 770 = \frac{22}{7} \times 14 \times 14 \times h \\ = > 770 = 22 \times 2 \times 14 \times h\end{gathered}

=>770=

7

22

×14×14×h

=>770=22×2×14×h

\begin{gathered} = > h = 770 \div 22 \times 2 \times 14 \\ = > h = \frac{5}{14} \\ = > h = 3.5cm \end{gathered}

=>h=770÷22×2×14

=>h=

14

5

=>h=3.5cm

height =3.5 cm

CSA =

\begin{gathered}2 \times \pi \times r \times h \\ = 2 \times \frac{22}{7} \times 14 \times 3.5 {cm}^{2} \\ = 308 {cm}^{2} \end{gathered}

2×π×r×h

=2×

7

22

×14×3.5cm

2

=308cm

2

TSA =

\begin{gathered}2 \times \pi \times r(h + r) \\ = 2 \times \frac{22}{7} \times 14 \times (3.5 + 14) {cm}^{2} \\ = 88 \times 17.5 {cm}^{2} \\ = 1540 {cm}^{2} \end{gathered}

2×π×r(h+r)

=2×

7

22

×14×(3.5+14)cm

2

=88×17.5cm

2

=1540cm

2