Question

1. find the surface area and volume:

what kind of solid is this?
what is the radius?
what is the slant height?
what is the height?
what is the surface area?
what is the volume?

Explanation:

Step1: Calculate the surface area

The surface area formula of a cone is \(S=\pi r(r + l)\), where \(r\) is the radius and \(l\) is the slant height.
Given \(r = 8\mathrm{cm}\), \(l=14\mathrm{cm}\)

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Step2: Calculate the volume

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.
Given \(r = 8\mathrm{cm}\), \(h = 11.4\mathrm{cm}\)

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Answer:

The surface area is approximately \(552.64\mathrm{cm}^2\) and the volume is approximately \(763.648\mathrm{cm}^3\)