Question

Find the surface area of each figure to the nearest tenth.

Answer 1

For the cylinder on the left-hand-side,

$\bf \textit{surface area of a cylinder}\\\\ S=2\pi r(h+r)\quad \begin{cases} r=radius\\ h=height\\ ------\\ h=10\\ r=5 \end{cases}\implies S=2\pi (5)(10+5)$

now, for the triangular prism on the right-hand-side,

notice is really just 2 triangles and 3 rectangles, stacked  up to each other at the edges.

the triangles have a base of 4, and a height of 1.5.

the rectangle on the left and the one on the right is a 6x2.5 rectangle.

the rectangle at the bottom, is a 4x6 rectangle.

adding their areas, is the area of the prism,

$\bf \stackrel{two~triangles}{2\left[\cfrac{1}{2}(4)(1.5) \right]}+\stackrel{left-right~rectangles}{2(6\cdot 2.5)}+\stackrel{bottom~rectangle}{4\cdot 6} \\\\\\ 6~~+~~30~~+~~24$