Question

Find the surface area and volume of the composite figure. Use 3.14 for π and round to the nearest tenth if needed.

Answer 1

$\huge \mathrm {➢ \: \: \: \: Answer }$

The above figure consists of three different shapes, that is :

• A hemisphere
• A Cylinder
• A Cone

Let's solve for surface area of whole figure :

1. Curved surface area of hemisphere : -

• radius (r) = 4 m

$\large \boxed{ \boxed{2\pi {r }^{2} }}$

$➢ \: \: 2 \times 3.14 \times 4 \times 4$

$➢ \: \: 100.48 \: m {}^{2}$

2. lateral surface area of Cylinder : -

• radius (r) = 4 m
• height (h) = 10 m

$\large \boxed {\boxed{2\pi rh}}$

$➢ \: \: 2 \times 3.14 \times 4 \times 10$

$➢ \: \: 251.2 \: { m}^{2}$

3. curved surface area of cone :

• radius (r) = 4 m
• height of cone (h') = 3 m.

$slant \: height = \sqrt{4 {}^{2} + 3 {}^{2} }$

(by Pythagoras theorem)

$\large \boxed { \boxed{c.s.a = \pi rl}}$

$➢ \: \: 3.14 \times 4 \times 5$

$62.8 \: m {}^{2}$

Surface area of the figure :

$➢ \: \: 100.48 + 251.2 + 62.8$

$➢ \: \: 414.48 \: \: m {}^{2}$

$➢ \: \: 414.5 \: m {}^{2} \: \: \: (approx)$

Now, let's solve for volume :

Volume of given figure will be combined volume of the all three shapes,

1. Volume of hemisphere :

$\boxed{ \boxed{\dfrac{2}{3} \pi {r}^{3} }}$

$➢ \: \: \dfrac{2}{3} \times 3.14 \times 4 \times 4 \times 4$

$➢ \: \: 133.97 \: \: { m}^{3}$

2. Volume of Cylinder :

$\large\boxed{ \boxed{ \pi{r}^{2}h }}$

$➢ \: \: 3.14 \times 4 \times 4 \times 10$

$➢ \: \: 502.4 \: m {}^{3}$

3. Volume of cone :

• height of cone (h') = 3 m

$\large \boxed {\boxed{ \frac{1}{3} \pi {r}^{2}h' }}$

$➢ \: \: \dfrac{1}{ 3} \times 3.14 \times 4 \times 4 \times 3$

$➢ \: \: 50.24 \: {m}^{3}$

The total volume of the given figure :

$➢ \: \: 133.97 + 502.4 + 50.24$

$➢ \: \: 686.61 \: {m}^{3}$

or

$➢ \: \: 686.6 \: \: m {}^{3} \: \: \: (approx)$

$\mathrm{✌TeeNForeveR✌}$

Answer 2

Answer:

Step-by-step explanation:

The shape consists of three parts: a half sphere, a round cylinder and a round cone.

The half sphere volume = 1/2 * 4/3 * π * (4)^3

= 32/3 π

The round cyllinder volume = π * (4)^2 * 10

= 160 π

The round cone volume = 1/3 * π * (4)^2 * 3

= 16 π

Adding them together, the volume of shape

= 32/3 π + 160π + 16π

= (32/3 + 160 + 16)*3.14

= 586.13

Similarly the surface area

= (4π4^2)/2 + 2π4*10 + π*4*5

= (32+80+25)*3.14

= 430.18