Question

PLEASE HELP ME AND EXPLAIN THIS PROBLEM TO ME CUZ I DON'T UNDERSTAND IT!! WILL GIVE BRAINLIEST!!

Answer 1

for the first one, let's notice something, its base has a diameter of 8 inches, meaning its radius is 4, and it has a slant height of 7 inches, thus

$\bf \textit{surface area of a cone}\\\\ SA=\pi rs+\pi r^2~~ \begin{cases} r=radius\\ s=slant~height\\[-0.5em] \hrulefill\\ r=4\\ s=7 \end{cases}\implies SA=\pi (4)(7)+\pi (4)^2 \\\\\\ SA=28\pi +16\pi \implies SA=44\pi \implies \stackrel{\pi =3.14}{SA=138.16}$

the 2nd one, is just a right-circular cylinder, with a diameter of 34, thus a radius of half that or 17, and a height of 27$\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=17\\ h=27 \end{cases}\implies V=\pi (17)^2(27) \\\\\\ V=7803\pi \implies \stackrel{\pi =3.14}{V=24501.42}$

the third one is a square pyramid, namely one of its faces is a square, so it'll be the one on the left-hand-side, the rest are just triangles.

we're looking for the lateral area, namely the area of the sides, namely excluding its base, well, this pyramid is resting on a triangular face, so we'll be excluding that and including the square and the other three triangles.

let's notice, the square is just an 8x8, and the triangles have a base of 8, and an altitutde/height of 22.

$\bf \stackrel{\textit{area of the square}}{(8\cdot 8)}~~~~+~~~~\stackrel{\textit{area of the three triangles}}{3\left[ \cfrac{1}{2}(8)(22) \right]}\implies 64+264\implies 328$