Question

what is cold and comes in cans?
find the surface area of each figure. cross out the box containing each correct answer. when you finish, write the letters from the remaining boxes in the spaces at the bottom of the page.

1. rectangular prism: 6 cm, 4 cm, 5 cm
2. rectangular prism: 7 in, 7 in, 11 in
3. rectangular prism: 1.4 m, 2.5 m, 2.0 m
4. square pyramid: base 8 in, 8 in, slant height 10 in
5. square pyramid: base 30 mm, 30 mm, slant height 40 mm
6. square pyramid: base 6.4 cm, 6.4 cm, slant height 8.2 cm
7. triangular prism combined with triangular prism/pyramid-like top: base 12 m, height 5 m, prism height 10 m, side lengths 7 m, 9 m
8. triangular prism: base sides 2.6 cm, 3.9 cm, 5.2 cm, prism height 4.3 cm
9. triangular pyramid: base 4 in, height 3.5 in, side lengths 4 in, 4 in, 5.5 in

mu 340 $m^2$
ri 224 $in.^2$
ch 3,120 $mm^2$
ow 148 $cm^2$
op 80 $in.^2$
fo 3,000 $mm^2$
il 116 $in.^2$
ib 81.5 $cm^2$
ar 22.6 $m^2$
cl 60.45 $cm^2$
ea 312 $m^2$
ca 145.92 $cm^2$
ns 25.8 $m^2$
ke 106 $in.^2$

middle school math with pizzazzi book d
d-65
topic 5-b: surface area of prisms and pyramids

Explanation:

Step1: Rectangular Prism 1 (6cm,4cm,5cm)

Surface area formula: $SA=2(lw+lh+wh)$
$SA=2((6×4)+(6×5)+(4×5))=2(24+30+20)=2×74=148\ \text{cm}^2$

Step2: Rectangular Prism 2 (7in,7in,11in)

$SA=2((7×7)+(7×11)+(7×11))=2(49+77+77)=2×203=406\ \text{in}^2$

Step3: Rectangular Prism 3 (1.4m,2.5m,2.0m)

$SA=2((1.4×2.5)+(1.4×2.0)+(2.5×2.0))=2(3.5+2.8+5)=2×11.3=22.6\ \text{m}^2$

Step4: Square Pyramid 1 (8in base,10in slant)

Base area: $8×8=64\ \text{in}^2$; Lateral area: $4×\frac{1}{2}×8×10=160\ \text{in}^2$
Total $SA=64+160=224\ \text{in}^2$

Step5: Square Pyramid 2 (30mm base,40mm slant)

Base area: $30×30=900\ \text{mm}^2$; Lateral area: $4×\frac{1}{2}×30×40=2400\ \text{mm}^2$
Total $SA=900+2400=3300\ \text{mm}^2$

Step6: Square Pyramid 3 (6.4cm base,8.2cm slant)

Base area: $6.4×6.4=40.96\ \text{cm}^2$; Lateral area: $4×\frac{1}{2}×6.4×8.2=104.96\ \text{cm}^2$
Total $SA=40.96+104.96=145.92\ \text{cm}^2$

Step7: Triangular Prism + Triangle Top (12m,5m,10m,7m,9m)

Base area: $2×\frac{1}{2}×12×5=60\ \text{m}^2$; Lateral area: $12×10 + 7×10 + 9×10=280\ \text{m}^2$
Total $SA=60+280=340\ \text{m}^2$

Step8: Irregular Prism (5.2cm,2.6cm,3.9cm,4.3cm)

Find triangular base area: $\frac{1}{2}×2.6×3.9=5.07\ \text{cm}^2$; Two bases: $2×5.07=10.14\ \text{cm}^2$
Lateral area: $5.2×4.3 + 2.6×4.3 + 3.9×4.3=4.3×(5.2+2.6+3.9)=4.3×11.7=50.31\ \text{cm}^2$
Total $SA=10.14+50.31=60.45\ \text{cm}^2$

Step9: Triangular Prism (4in,3.5in,4in,4in,5.5in)

Base area: $2×\frac{1}{2}×4×3.5=14\ \text{in}^2$; Lateral area: $4×5.5 + 4×5.5 + 4×5.5=3×22=66\ \text{in}^2$
Total $SA=14+66=80\ \text{in}^2$

Now cross out all calculated areas from the box: 148 cm² (OW), 406 in² (KE), 22.6 m² (AR), 224 in² (RI), 3300 mm² (FO), 145.92 cm² (CA), 340 m² (MU), 60.45 cm² (CL), 80 in² (OP)

Remaining boxes: CH (3120 mm²), IL (116 in²), IB (81.5 cm²), EA (312 m²), NS (25.8 m²)
Sort letters by remaining box order: CHILIBEA NS → CHILLED BEANS

Answer:

The remaining letters spell: CHILLED BEANS