Question

Find the volume of the composite solid if the diameter is 8.7 yards. Round your answer to the nearest hundredth.

A.
220.76 yd3
B.
429.88 yd3
C.
535.02 yd3
D.
693.55 yd3

Answer 1

The closest answer is D. 693.55 yd3
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Answer 2

Answer: D. 693.55 yd3

Explanation:

Given: The diameter of the composite solid = 8.7 yards

Then , the radius of the composite solid =
`(8.7)/(2)=4.35\ \text{yards}`

Height of cylinder = 9 yards

Height of cone = 8 yards

The volume of cylinder is given by :-

`V_1=\pi r^2h\\\\\Rightarrow V_1=(3.14159265359)(4.35)^2(9)\\\\\Rightarrow V_1=535.021082888{ yards}^3`

The volume of cone is given by :-

`V_2=(1)/(3)\pi r^2h\\\\\Rightarrow V=(1)/(3)(3.14159265359)(4.35)^2(8)\\\\\Rightarrow V=158.5247653\text{ yards}^3`

Now, Volume of the composite figure will be :

`V=V_1+V_2\\\\\Rightarrow\ V=535.021082888+158.5247653\\\\\Rightarrow\ V=693.545848188\approx693.55\text{ yards}^3`