6.4.1 Surface Area of Three Dimensional Shapes, PT3 Focus Practice - Mathematics

6.4.1 Surface Area of Three Dimensional Shapes, PT3 Focus Practice

Question 1:

Diagram below shows closed right cylinder.

Calculate the total surface area, in cm², of the cylinder.

(π = \frac{22}{7})

$(π = \frac{22}{7})$

Solution:

Total surface area

= 2(πr²) + 2πrh

\begin{array}{l} = (2 \times \frac{22}{7} \times 7^{2}) + (2 \times \frac{22}{7} \times 7 \times 20) \\ = 308 + 880 \\ = 1188 c m^{2} \end{array}

$\begin{array}{l} = (2 \times \frac{22}{7} \times 7^{2}) + (2 \times \frac{22}{7} \times 7 \times 20) \\ = 308 + 880 \\ = 1188 c m^{2} \end{array}$

Question 2:

Diagram below shows a right prism with right-angled triangle ABC as its uniform cross section.

Calculate the total surface area, in cm², of the prism.

Solution:

\begin{array}{l} A B = \sqrt{5^{2} - 3^{2}} \\ = \sqrt{25 - 9} \\ = \sqrt{16} \\ = 4 c m \end{array}

$\begin{array}{l} A B = \sqrt{5^{2} - 3^{2}} \\ = \sqrt{25 - 9} \\ = \sqrt{16} \\ = 4 c m \end{array}$

Total surface area

= 2 (½× 3 × 4) + (3 × 10) + (4 × 10) + (5 × 10)

= 12 + 30 + 40 + 50

= 132 cm²

Question 3:

The diagram shows a cone. The radius of its base is 3.5 cm and its slant height is 6 cm. Find the area of its curved surface.
( π= 22 7 )

Solution:

Area of curved surface

= π × radius of base × slant height

= πrs

\begin{array}{l} = \frac{22}{7} \times 3.5 \times 6 \\ = 66 c m^{2} \end{array}

$\begin{array}{l} = \frac{22}{7} \times 3.5 \times 6 \\ = 66 c m^{2} \end{array}$