Question

21 identify the 3 - d shapes with a surface area less than 100 cm².
a. sphere (radius = 3 cm)
b. rectangular prism (length = 10 cm, width = 4 cm, height = 5 cm)
c. cylinder (radius = 3 cm, height = 8 cm)
d. triangular prism (base area = 9 cm², perimeter of base = 9 cm, height = 5 cm)

Explanation:

Step1: Calculate the surface area of the sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\). Given \(r = 3\mathrm{cm}\), then \(S=4\pi\times3^{2}=36\pi\approx36\times 3.14 = 113.04\mathrm{cm}^{2}\)

Step2: Calculate the surface area of the rectangular prism

The formula for the surface area of a rectangular prism is \(S=2(lw + lh+wh)\). Given \(l = 10\mathrm{cm}\), \(w = 4\mathrm{cm}\), \(h = 5\mathrm{cm}\), then \(S=2\times(10\times4 + 10\times5+4\times5)=2\times(40 + 50+20)=2\times110 = 220\mathrm{cm}^{2}\)

Step3: Calculate the surface area of the cylinder

The formula for the surface area of a cylinder is \(S = 2\pi r(r + h)\). Given \(r = 3\mathrm{cm}\), \(h = 8\mathrm{cm}\), then \(S=2\pi\times3\times(3 + 8)=6\pi\times11\approx6\times3.14\times11=207.24\mathrm{cm}^{2}\)

Step4: Calculate the surface area of the triangular prism

The formula for the surface area of a triangular prism is \(S=2B+Ph\). Given \(B = 9\mathrm{cm}^{2}\), \(P = 9\mathrm{cm}\), \(h = 5\mathrm{cm}\), then \(S=2\times9+9\times5=18 + 45=63\mathrm{cm}^{2}\)

Answer:

d. Triangular Prism (Base Area = 9 cm², Perimeter of Base = 9 cm, Height = 5 cm)