Question

The figure shows a solid consisting of a
pyramid of height 28 cm fastened to a
cuboid of height 40 cm and a square base
of sides 30 cm each. Find

the total surface area of the solid
(leave your answer correct to 2 decimal
places).
​

Answer 1

Step-by-step explanation:

exposed area of cuboid = 4* the area of the side walls (rectangles) + area of the square base

the side walls are rectangles with sides: 40 cm and 30 cm

exposed area of cuboid = 4 * 40 * 30 + 30^2 = 5700 cm²

using the Pythagorean Theorem we find

slant height of pyramid s = √(28² + (30/2)²) = 31.8 cm, so the

exposed area of pyramid = 4 * (area of the triangle with base 30 and height s)

exposed area of pyramid = 4 * 30 * 31.8 / 2 = 1906 cm²

the total area of the solid = exposed area of cuboid + exposed area of pyramid

Total area of solid = 5700 + 1906 = 7606 cm²

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