Question

3.
lateral area:
total surface area:
5.
lateral area:
total surface area:

Explanation:

Problem 3 (Rectangular Prism with dimensions 32 in, 10 in, 18 in)

Lateral Area

Step1: Recall lateral area formula for rectangular prism

The lateral surface area (LSA) of a rectangular prism is given by \( LSA = 2h(l + w) \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 32 \) in, \( w = 10 \) in, \( h = 18 \) in.

Step2: Substitute values into formula

\( LSA = 2\times18\times(32 + 10) \)
\( = 36\times42 \)
\( = 1512 \) square inches.

Total Surface Area

Step1: Recall total surface area formula for rectangular prism

The total surface area (TSA) of a rectangular prism is given by \( TSA = 2(lw + lh + wh) \).

Step2: Substitute values (\( l = 32 \), \( w = 10 \), \( h = 18 \))

\( TSA = 2\times(32\times10 + 32\times18 + 10\times18) \)
\( = 2\times(320 + 576 + 180) \)
\( = 2\times1076 \)
\( = 2152 \) square inches.

Problem 5 (Rectangular Prism with dimensions 18 yd, 8 in, 10 in) - Note: Units should be consistent, assuming it's a typo and all in inches or all in yards. Let's assume all in inches (correcting 18 yd to 18 in for consistency, or if yd is correct, convert to inches: 18 yd = 648 in, but likely a typo). Let's proceed with \( l = 18 \) in, \( w = 8 \) in, \( h = 10 \) in.

Lateral Area

Step1: Use lateral area formula \( LSA = 2h(l + w) \)

Here, \( l = 18 \) in, \( w = 8 \) in, \( h = 10 \) in.

Step2: Substitute values

\( LSA = 2\times10\times(18 + 8) \)
\( = 20\times26 \)
\( = 520 \) square inches.

Total Surface Area

Answer:

s:

Problem 3

• Lateral Area: \( \boldsymbol{1512} \) square inches
• Total Surface Area: \( \boldsymbol{2152} \) square inches

Problem 5 (assuming 18 in, 8 in, 10 in)

• Lateral Area: \( \boldsymbol{520} \) square inches
• Total Surface Area: \( \boldsymbol{808} \) square inches

(Note: If 18 yd is correct, convert 18 yd to 648 in first, then recalculate. For example, LSA for 18 yd (648 in), 8 in, 10 in: \( LSA = 2\times10\times(648 + 8)=20\times656 = 13120 \) square inches, and TSA \( = 2\times(648\times8 + 648\times10 + 8\times10)=2\times(5184 + 6480 + 80)=2\times11744 = 23488 \) square inches. But the mixed units (yd and in) suggest a typo, so the first calculation with all in inches is more reasonable.)