a. Cube b. trapezoid c. pentagon d. square

1. Describe the cross section.

EOC Practice

2. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number.

EOC Practice

a. 35 cm ; 364 cm b. 70 cm ; 364 cm

 

c. 35 cm ; 266 cm d. 70 cm ; 266 cm

𝑺 . 𝑨 .=𝑷𝒉+𝟐 𝒍𝒘𝒍=¿¿𝒘

𝒉=¿

Base Area

Lateral Area

¿𝟔𝟗 .𝟕𝟐+𝟐 𝒍𝒘¿𝟕𝟎+𝟐(𝟏𝟒)(𝟕)

¿𝟐𝟔𝟔

𝑺 . 𝑨 .=𝑷𝒉+𝟐𝑩

5

2

5.39

26

Not drawn to scale

3. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.

EOC Practice

a. 322 m² ; 327 m² b. 296 m² ; 342 m²

 c. 296 m² ; 332 m² d. 322 m² ; 332 m²

𝑺 . 𝑨 .=𝑷𝒉+𝟐𝑩

¿𝟑𝟑𝟐𝒎𝟐

4. Find the surface area of the cylinder in terms of .

EOC Practice

a. 350 cm² b. 896 cm²

 c. 602 cm² d. 644 cm²

𝒓=𝟕

5. Find the surface area of the regular pyramid shown to the nearest whole number.

EOC Practice

5 ft

5 ft

7 ft

Not drawn to scale

a. 165 ft² b. 95 ft²

 c. 70 ft² d. 28 ft²

𝒃=¿¿𝒘

¿𝓵

6. Find the slant height of the pyramid shown, to the nearest tenth.

EOC Practice

7 mm

3 mm

3 mm

x

Not drawn to scale

a. 6.3 mm b. 7.6 mm c. 4.1 mm d. 7.2 mm

𝒃=¿¿𝒘

¿𝒉¿𝓵

𝒄𝟐=𝒂𝟐+𝒃𝟐𝓵𝟐=(𝟏𝟐 𝒃)𝟐

+𝒉𝟐

𝟏 .𝟓𝓵𝟐= (𝟏 .𝟓 )𝟐+(𝟕)𝟐𝓵𝟐=𝟓𝟏 .𝟐𝟓𝓵=√𝟓𝟏 .𝟐𝟓  𝓵=𝟕 .𝟏𝟓𝟖𝟗

7. Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.

EOC Practice

a. 210 in² b. 240 in² c. 42 in² d. 420 in²

𝑳 . 𝑨 .=𝟏𝟐

(𝟓)(𝟔)(𝟏𝟒 )𝓵=𝟏𝟒=𝒉

𝒃=𝟔

8. Find the surface area of the cone in terms of .

EOC Practice

17 cm

3 cm

Not drawn to scale

a. 111 cm² b. 57 cm²

 c. 60 cm² d. 55.5 cm²

9. Find the slant height of the cone to the nearest whole number.

EOC Practice

a. 21 m b. 19 m c. 24 m d. 23 m

19 m

10 m

Not drawn to scale

𝟏𝟗𝓵 𝒄𝟐=𝒂𝟐+𝒃𝟐𝓵𝟐=𝒉𝟐+𝒓𝟐𝓵𝟐=(𝟏𝟗)𝟐+(𝟏𝟎)𝟐𝓵𝟐=𝟒𝟔𝟏𝓵=√𝟒𝟔𝟏𝓵=𝟐𝟏 .𝟒𝟕

*** Find the Surface Area of the sphere shown. Give each answer rounded to the nearest cubic unit. 

EOC Practice

𝑺 . 𝑨 .=𝟒𝝅𝒓 𝟐

𝑺 . 𝑨 .=𝟒(𝟑 .𝟏𝟒)(𝟕)𝟐

𝑺 . 𝑨 .=𝟔𝟏𝟓 .𝟒𝟒𝑺 . 𝑨 .=𝟔𝟏𝟓𝒄𝒎 ²

10. Find the volume of the given prism. Round to the nearest tenth if necessary.

EOC Practice

a. 308.9 cm³ b. 308.2 cm³ c. 312.8 cm³ d. 302.9 cm³

𝑽=𝒃𝒘𝒉𝑽=𝒍𝒘 𝒉𝑽=(𝟏𝟑 .𝟐)(𝟑 .𝟗)(𝟔)𝑽=𝟑𝟎𝟖 .𝟖𝟖

𝑽=𝑩𝒉

11. Find the volume of the given prism. Round to the nearest tenth if necessary.

EOC Practice

a. 17 m³ b. 34 m³ c. 8.5 m³ d. 1 m³

𝑽=𝑩𝒉𝑽=(𝟏𝟐 𝒃𝒉) (𝒉 )

𝑽=(𝟏𝟐 (𝟏)(𝟐)) (𝟏𝟕)

𝑽=𝟏𝟕𝒎𝟑

12. The volume of a cylinder is 980 in. The height of the cylinder is 20 in. What is the radius of the cylinder?.

EOC Practice

a. 7 in b. 49 in c. 327 in d. 18 in

𝑽=𝟗𝟖𝟎 𝝅𝒉=𝟐𝟎𝒓=?

𝑽=𝝅 𝒓𝟐𝒉𝟗𝟖𝟎𝝅=𝝅𝒓 𝟐(𝟐𝟎)

𝟐𝟎𝝅𝟒𝟗=𝒓𝟐

𝟕=𝒓

𝟐𝟎𝝅

𝑽=𝑩𝒉

13. Find the volume of the cylinder in terms of .

EOC Practice

a. 27 in.³ b. 27 in.³  c. 54 in.³ d. 324 in.³

h = 6 in. and r = 3 in.

𝑽=𝝅 𝒓𝟐𝒉

h = 6 in. and r = 3 in.

𝑽=𝝅 (𝟑 )𝟐(𝟔)𝑽=𝟓𝟒 𝝅

𝑽=𝑩𝒉

14. Find the volume of the cylinder in terms of .

EOC Practice

a. 704 in.³ b. 88 in.³  c. 176 in.³ d. 352 in³

𝑽=𝝅 𝒓𝟐𝒉𝑽=𝝅 (𝟖 )𝟐(𝟏𝟏)𝑽=𝟕𝟎𝟒 𝝅

𝑽=𝑩𝒉

15. Find the height of the cylinder.

EOC Practice

a. 2.4 in. b. 7.2 in. c. 14.4 in. d. 4.8 in.

𝑽=𝝅 𝒓𝟐𝒉𝟐𝟕𝟏 .𝟒=𝟑 .𝟏𝟒(𝟔)𝟐𝒉𝟐𝟕𝟏 .𝟒=𝟏𝟏𝟑 .𝟎𝟒𝒉𝟐 .𝟒=𝒉

𝑽=𝑩𝒉

16. Find the volume of the composite space figure to the nearest whole number.

EOC Practice

a. 416 mm³ b. 705 mm³  c. 1294 mm³ d. 944 mm³

𝑽=𝑩𝒉

𝑽=𝟏𝟐

(𝝅𝒓 𝟐𝒉  )+𝒃𝒘𝒉  𝑽=(𝟏𝟐 (𝝅𝒓𝟐)+𝒍𝒘)𝒉  

𝑽=(𝟏𝟐 (𝟑 .𝟏𝟒×𝟒 .𝟓𝟐 )+𝟗×𝟔)𝟏𝟏𝑽=(𝟑𝟏 .𝟕𝟗𝟐𝟓+𝟓𝟒 )𝟏𝟏𝑽=𝟗𝟒𝟑 .𝟕𝟏𝒎𝒎𝟑

17. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

EOC Practice

a. 126 cm³ b. 907.5 cm³ c. 605 cm³ d. 55 cm³

11 cm11 cm

15 cm

Not drawn to scale

𝑽=𝟏𝟑𝑩𝒉

𝑽=𝟏𝟑𝒍𝒘 𝒉

𝑽=𝟏𝟑

(𝟏𝟏)(𝟏𝟏)(𝟏𝟓)

𝑽=𝟔𝟎𝟓

18. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

EOC Practice

a. 1280 ft³ b. 85.3 ft³  c. 1920 ft³ d. 3840 ft³

𝑽=𝟏𝟑𝑩𝒉

𝑽=𝟏𝟑𝒍𝒘 𝒉

𝒄𝟐=𝒂𝟐+𝒃𝟐𝓵𝟐=𝒉𝟐+𝒓𝟐

𝟏𝟕𝟐=𝒉𝟐+𝟖𝟐

𝟐𝟖𝟗=𝒉𝟐+𝟔𝟒𝟐𝟐𝟓=𝒉𝟐

√𝟐𝟐𝟓=𝒉𝟏𝟓=𝒉

𝑽=𝟏𝟑

(𝟏𝟔)(𝟏𝟔)(𝟏𝟓 )

𝑽=𝟏𝟐𝟖𝟎

19. Find the volume of the right cone shown as a decimal rounded to the nearest tenth

EOC Practice

a. 8821.6 m³ b. 2205.4 m³  c. 3308.1 m³ d. 980.2 m³

26 m

18 m

Not drawn to scale

𝑽=𝟏𝟑𝑩𝒉

𝑽=𝟏𝟑

(𝝅𝒓 𝟐)𝒉

𝑽=𝟏𝟑

(𝝅 (𝟗 )𝟐 )𝟐𝟔𝑽=𝟐𝟐𝟎𝟓 .𝟑𝟗

20. Find the volume of the oblique cone shown. Round to the nearest tenth.

EOC Practice

a. 108.9 in.³ b. 707.9 in.³  c. 1061.9 in.³ d. 980.2 in.³

16 in.

13 in.

Not drawn to scale

𝑽=𝟏𝟑𝑩𝒉

𝑽=𝟏𝟑

(𝝅𝒓 𝟐)𝒉

𝑽=𝟏𝟑

(𝝅 (𝟔 .𝟓 )𝟐 )𝟏𝟔𝑽=𝟕𝟎𝟕 .𝟗𝟎

21. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 

EOC Practice

a. 11,494 cm³ b. 359 cm³  c. 1,437 cm³ d. 205 cm³

𝑽=𝟒𝟑𝝅𝒓𝟑

𝑽=𝟒𝟑𝝅 (𝟕)𝟑

𝑽=𝟏𝟒𝟑𝟔 .𝟕𝟓

22. The volume of a sphere is 5000 m . What is the surface area of the sphere to the nearest square meter?  

EOC Practice

a. 62,832 m² b. 1517 m²  c. 3033 m² d. 195 m²

𝑽=𝟒𝟑𝝅𝒓𝟑

𝟓𝟎𝟎𝟎 𝝅=𝟒𝟑𝝅 𝒓𝟑

𝟑𝟕𝟓𝟎=𝒓 𝟑

𝟑√𝟑𝟕𝟓𝟎=𝒓𝟏𝟓 .𝟓𝟑𝟔𝟏=𝒓

𝑺 . 𝑨 .=𝟒𝝅𝒓 𝟐

𝑺 . 𝑨 .=𝟒𝝅 (𝟏𝟓 .𝟓𝟑𝟔𝟏)𝟐

𝑺 . 𝑨 .=𝟑𝟎𝟑𝟑 .𝟏𝟒𝟗