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3 problems match “volume of prisms”. Clear

Volume of a regular pentagonal prism ●○○○○ 10 ptsA right prism has regular pentagons as its bases. The side length of each pentagonal base is 4 cm and the height of the prism is 11 cm. Find the volume of the prism in cubic cm. Use the area of a regular pentagon $\approx 1.720477\,s^2$ for side length $s$ . Round to two decimal places.
Diagonal of a rectangular face ●●○○○ 20 ptsA regular right pentagonal prism has a length (the distance between its two pentagonal bases) of 18.9 cm and a volume of 452.7 cm $^3$ . Find the diagonal length of one of its rectangular faces, in cm, rounded to the nearest millimetre (one decimal place). Use the area of a regular pentagon $\approx 1.720477\,s^2$ for side length $s$ .
Minimal surface area for fixed volume ●●●○○ 50 ptsA regular right pentagonal prism has a volume of $278.3105$ cubic cm. Let $x$ be the side length of the regular pentagonal bases and $y$ the length (height) of the prism, in cm. Find the values of $x$ and $y$ that minimize the total surface area. Use the area of a regular pentagon $\approx 1.720477\,x^2$ . Round each value to four decimal places.