4 The diagram shows a concrete solid used in construction.
Find the volume of the solid.
Give your answer to 3 significant figures.
15 m
7 m
m

Volume of figure = 289 m³

Step-by-step explanation:

Given figure is in the half cylindrical shape.

So calculate the volume of the whole cylinder first then half the volume.

Since, formula to calculate the volume of a cylinder is,

V = πr²h

Here, r = radius of the cylinder

h = height of the cylinder

Therefore, volume of a cylinder with 'r' = m and h = 15 m will be,

V = π(3.5)²(15)

V = 577.268 m³

Half of the volume =

                               = 288.634 m³

                                ≈ 289 m³

Therefore, volume of the figure shown in the picture = 289 m³

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°