A solid is formed by a pyramid mounted on a cube, the base coinciding with cube's upper face. Side of cube is $16 c m$ $16 cm$ and the apothem of the pyramid is $17 c m$ $17 cm$ . Calculate: the total surface area, the volume and mass knowing is made wood $0.65 \frac{g}{c m^{3}}$ $0.65 g/(cm^3)$ ?

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Answer 1 · 2018-06-02T03:49:22

Total Surface Area: $\ color(green)(T S A = "1824 cm"^2)$

Volume: $\ color(maroon)(V_t = V_c + V_p = "23296 cm"^3)$

Mass of wood: $\ color(blue)(m = d * V_t = 15,142.4 \ "g")$

Side $= a = "16 cm"$ , apothem $= l = "17 cm"$

Total Surface Area = Base Area of Cube + Lateral Surface Area of the Cube + Surface Area of Pyramid

Base Area of Cube $A_b = a^2 = "256 cm"^2$

Lateral Surface Area of Cube $A_c = 4 a^2 = "1024 cm"^2$

Surface Area of Pyramid $= A_p = 4 * (a/2) * l = 4 * 8 * 17 = "544 cm"^2$

$T S A = 256 + 1024 + 544 = "1824 cm"^2$

$"Total Volume" \ (V_t) = "Volume of Cube" \ (V_c) + "Volume of Pyramid" \ (V_p)$

$V_c = a^3 = 16^3 = "4096 cm"^3$

$V_p = (1/3) * a^2 * h = (1/3) * a^2 * sqrt(l^2 - (a/2)^2)$

$V_p = (1/3) * 16^2 * sqrt(17^2 - 8^2)$

$V_p = (1/3) * 256 * 225 = "19200 cm"^3$

$"Volume" \ V_t = V_c + V_p = 4096 + 19200 = "23296 cm"^3$

Mass of Wood $m = "density" * "volume"$

$m = d * V_t = 0.65 * 23296 = 15,142.4$ $"g"$

A solid is formed by a pyramid mounted on a cube, the base coinciding with cube's upper face. Side of cube is 16 cm16cm16 cm and the apothem of the pyramid is 17 cm17cm17 cm. Calculate: the total surface area, the volume and mass knowing is made wood 0.65 g/(cm^3)0.65gcm30.65 g/(cm^3)?