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jeyben [28]
3 years ago
5

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

Mathematics
2 answers:
inn [45]3 years ago
7 0

\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✌}

Vesnalui [34]3 years ago
3 0

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

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