# Can you help me ?

Mar 14, 2018

#### Explanation:

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Problem $4$:

This is a pyramid sitting atop a rectangular box. We can calculate the volume of each separately and add them together:

${V}_{\text{Box}} = l \cdot w \cdot h$ where $l , w , \mathmr{and} h$ are length, width, and height of the box:

${V}_{\text{Box}} = \left(6\right) \left(5\right) \left(2\right) = 60$ $C {m}^{3}$

${V}_{P y r a m i d} = \frac{1}{3} A r e {a}_{B a s e} H e i g h t = \frac{1}{3} \left(6\right) \left(5\right) \left(1.5\right) = 15$ $C {m}^{3}$

Total Volume $= 60 + 15 = 75$ $C {m}^{3}$

Problem $5$:

This is a cone sitting atop a cylinder. We can calculate the volume of each separately and add them together:

${V}_{\text{Cone}} = \frac{1}{3} A r e {a}_{B a s e} \cdot H e i g h t$

$A r e {a}_{B a s e} = A r e {a}_{\text{Circle}} = \pi {r}^{2}$ where $r$ is the radius

${V}_{\text{Cone}} = \frac{1}{3} \pi {\left(6\right)}^{2} \left(9\right) = 108 \pi$ ${m}^{3}$

${V}_{\text{Cylinder}} = A r e {a}_{B a s e} \cdot H e i g h t$

${V}_{\text{Cylinder}} = \pi {\left(6\right)}^{2} \left(6\right) = 216 \pi$ ${m}^{3}$

Total Volume $= 108 \pi + 216 \pi = 324 \pi = 1 , 018$ ${m}^{3}$

Mar 14, 2018

Q4 $= 75$ $c {m}^{3}$

Q5 $= 324 \pi$ ${m}^{3}$

#### Explanation:

Q4.
we separete into two calculation.

Total Volume =Volume cuboid + volume pyramid.

$= \left(w i \mathrm{dt} h \cdot \le n > h \cdot h e i g h t\right)$ + (1/3 * base area *height)

$= \left(5 \cdot 6 \cdot 2\right) + \left(\frac{1}{3} \cdot \left(5 \cdot 6 \cdot 1.5\right)\right)$

$= 60 + 15$
$= 75$ $c {m}^{3}$

Q5.
we separete into two calculation.

Total Volume =Volume cylinder + volume cone.

$= \pi \cdot {r}^{2} \cdot h + \frac{1}{3} \pi \cdot {r}^{2} h$

$= \pi \cdot {6}^{2} \cdot 6 + \frac{1}{3} \pi \cdot {6}^{2} \cdot 9$

$= 216 \pi + 108 \pi$

$= 324 \pi$ ${m}^{3}$