Certainly! Let's solve each part of Question 1.

1a. Surface Area of a Rectangular Prism

Given:

• Length ($l$) = 3.4 cm
• Width ($w$) = 2.1 cm
• Height ($h$) = 1.7 cm

Formula: $\text{Surface Area} = 2lw + 2lh + 2wh$

Solution: $\text{Surface Area} = 2(3.4 \times 2.1) + 2(3.4 \times 1.7) + 2(2.1 \times 1.7)$ $= 2(7.14) + 2(5.78) + 2(3.57)$ $= 14.28 + 11.56 + 7.14 = 32.98 \text{ cm}^2$

1b. Surface Area of a Triangular Prism

Given:

• Base of triangle = 4 cm
• Height of triangle = 3 cm
• Length/Height of prism = 8 cm

Formula: $\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}$ Step 1: Calculate the area of the triangle base: $\text{Base Area} = \frac{1}{2} \times 4 \times 3 = 6 \text{ cm}^2$

Step 2: Find the perimeter of the triangular base: Assume the triangular base is equilateral, so each side is 4 cm. $\text{Perimeter} = 4 + 4 + 4 = 12 \text{ cm}$

Step 3: Substitute into the surface area formula: $\text{Surface Area} = 2(6) + 12(8)$ $= 12 + 96 = 108 \text{ cm}^2$

1c. Volume of a Cylinder

Given:

• Radius ($r$) = 5 cm
• Height ($h$) = 12 cm

Formula: $\text{Volume} = \pi r^2 h$

Solution: $\text{Volume} = \pi (5)^2(12) = \pi (25)(12) = 300\pi \text{ cm}^3$

1d. Surface Area of a Cylinder

Given:

• Radius ($r$) = 5 cm
• Height ($h$) = 12 cm

Formula: $\text{Surface Area} = 2\pi rh + 2\pi r^2$

Solution: $\text{Surface Area} = 2\pi(5)(12) + 2\pi(5)^2$ $= 120\pi + 50\pi = 170\pi \text{ cm}^2$

1e. Surface Area of a Square Pyramid

Given:

• Base side length ($s$) = 6 cm
• Slant height ($l$) = 10 cm

Formula: $\text{Surface Area} = s^2 + 2sl$

Solution: $\text{Surface Area} = (6)^2 + 2(6)(10)$ $= 36 + 120 = 156 \text{ cm}^2$

1f. Volume of a Square Pyramid

Given:

• Base side length ($s$) = 6 cm
• Height ($h$) = 8 cm

Formula: $\text{Volume} = \frac{1}{3} \times s^2 \times h$

Solution: $\text{Volume} = \frac{1}{3} \times (6)^2 \times 8$ $= \frac{1}{3} \times 36 \times 8 = 96 \text{ cm}^3$

1g. Volume of a Cone

Given:

• Radius ($r$) = 4 cm
• Height ($h$) = 9 cm

Formula: $\text{Volume} = \frac{1}{3} \pi r^2 h$

Solution: $\text{Volume} = \frac{1}{3} \pi (4)^2(9)$ $= \frac{1}{3} \pi (16)(9) = 48\pi \text{ cm}^3$

All these parts have been solved using the respective formulas for surface area and volume of the given shapes.

If you need any clarifications or more detailed steps, feel free to ask!

Here are five related questions you can consider:

1. What would be the surface area of the rectangular prism if the height was increased by 2 cm?
2. How does the volume of the cylinder change if the radius is doubled?
3. If the slant height of the square pyramid is reduced by 2 cm, what will be its new surface area?
4. What happens to the volume of the cone if the height is halved?
5. How would the surface area of the triangular prism change if the length of the prism is doubled?

Tip: When dealing with surface areas and volumes, always ensure the dimensions are in the same units before applying the formulas.