Question

34. A solid is in the form of a cylinder with hemispherical ends on both sides. The height and the
diameter of cylinder are 10 cm and 7 cm respectively. Find the volume of the solid.​

Answer 1

Answer:

$564.8 \: {cm}^{3}$

Step-by-step explanation:

$\huge\underline\mathtt{\red{Let's \ do \ it !!}}$

Given:-

$\implies$ A cylinder with hemispherical ends on both the sides.

$\implies$ Diameter of the cylinder = Diameter of both the hemispheres, d = 7 cm

$\implies$ Radius, r = $\frac{7}{2}$ cm.

$\implies$ Height of the cylinder, h = 10cm

$\therefore$ Required volume of the solid is Volume of cylinder + 2(Volume of hemisphere)

Volume of cylinder:-

$\hookrightarrow$ $\Large\pi {r}^{2} h$

$\implies$ Volume = $\frac{22}{7}$ × ${\frac{7}{2}^{2}}$ × 10

$\implies$ $\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 10$

$\implies$ 11 × 7 × 5

$\implies$ 385 ${cm}^{3}$

Volume of hemisphere:-

$\hookrightarrow$ $\Large \frac{2}{3} \pi {r}^{3}$

$\implies$ $vol. = \frac{2}{3} \times \frac{22}{7} \times {( \frac{7}{2}) }^{3}$

$\implies$ $\frac{2}{3} \times \frac{22}{7} \times \frac{343}{8}$

$\implies$ $\frac{49 \times 11}{6} = 89.9 \: {cm}^{3} (approx.)$

Now,

Required volume:-

$\implies$ Volume of cylinder + 2(Volume of hemisphere)

$\implies$ 385 + 2(89.9)

$\implies$ 385 + 179.8

$\implies$ $564.8 \: {cm}^{3}$

Answer 2

Answer:

tep-by-step explanation:

\huge\underline\mathtt{\red{Let's \ do \ it !!}}Let′s do it!!

Given:-

\implies⟹ A cylinder with hemispherical ends on both the sides.

\implies⟹ Diameter of the cylinder = Diameter of both the hemispheres, d = 7 cm

\implies⟹ Radius, r = \frac{7}{2}27 cm.

\implies⟹ Height of the cylinder, h = 10cm

\therefore∴ Required volume of the solid is Volume of cylinder + 2(Volume of hemisphere)

Volume of cylinder:-

\hookrightarrow↪ \Large\pi {r}^{2} hπr2h

\implies⟹ Volume = \frac{22}{7}722 × {\frac{7}{2}^{2}}272 × 10

\implies⟹ \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 10722×27×27×10

\implies⟹ 11 × 7 × 5

\implies⟹ 385 {cm}^{3}cm3

Volume of hemisphere:-

\hookrightarrow↪ \Large \frac{2}{3} \pi {r}^{3}32πr3

\implies⟹ vol. = \frac{2}{3} \times \frac{22}{7} \times {( \frac{7}{2}) }^{3}vol.=32×722×(27)3

\implies⟹ \frac{2}{3} \times \frac{22}{7} \times \frac{343}{8}32×722×8343

\implies⟹ \frac{49 \times 11}{6} = 89.9 \: {cm}^{3} (approx.)649×11=89.9cm3(approx.)

Now,

Required volume:-

\implies⟹ Volume of cylinder + 2(Volume of hemisphere)

\implies⟹ 385 + 2(89.9)

\implies⟹ 385 + 179.8

\implies⟹ 564.8 \: {cm}^{3}564.8cm3

hope it helps uh