Volume of combined solids

Grade 10 Math Worksheet - Building Confidence

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Circle the best answer.

1.
Ari's silo is a cylinder 8 m across and 10 m tall, topped by a half-ball. Which expression gives its volume in m³?
- π·4²·10
- π·8²·10 + (2/3)π·8³
- π·4²·10 + (4/3)π·4³
- π·4²·10 + (2/3)π·4³
2.
Bo's toy rocket is a can 6 in across and 10 in tall with a cone tip 4 in tall. Which expression gives its volume in in³?
- π·3²·10 = 90π
- π·6²·10 + (1/3)π·6²·4 = 408π
- π·3²·10 + (1/3)π·3²·4 = 102π
- π·3²·10 + π·3²·4 = 126π
3.
A block is 10 cm by 8 cm by 6 cm. Esme drills a round hole 4 cm across straight through the 6 cm height. Which expression gives the volume left?
- 10·8·6 − π·2²·6 = 480 − 24π
- 10·8·6 = 480
- 10·8·6 − π·4²·6 = 480 − 96π
- 10·8·6 + π·2²·6 = 480 + 24π
4.
Jun's treat is a cone 6 cm across and 9 cm tall with a half-ball scoop of the same width on top. Which expression gives its volume?
- (1/3)π·6²·9 + (2/3)π·6³
- (1/3)π·3²·9 + (4/3)π·3³ = 63π
- (1/3)π·3²·9 + (2/3)π·3³ = 45π
- π·3²·9 + (2/3)π·3³ = 99π
5.
A tent is a box 4 m by 4 m by 2 m with a pyramid roof. Each sloping face has slant height 2.5 m. Kira finds the volume. What is it?
- 56 m³: the roof taken as 4 × 4 × 1.5
- 8 m³, the roof alone
- 45⅓ m³: roof height taken as the slant, 2.5 m
- 40 m³: roof height √(2.5² − 2²) = 1.5 m
6.
A funnel is a cone with radius 3 cm and slant height 5 cm. Luz finds the volume. What is it?
- 12π cm³: height √(5² − 3²) = 4 cm
- 4 cm: the height
- 36π cm³: π·3²·4, no third
- 15π cm³: height taken as the slant, 5 cm
7.
Sketch, not to scale. A straight stack of coins has volume 100 cm³. Pia slides the coins so the stack leans, with the same coins and the same height. What is the volume now?
- Still 100 cm³: every layer keeps the same area
- Less than 100 cm³: the leaning stack looks smaller
- More than 100 cm³: the slanted side is longer
- 100 × cos of the lean angle, because the stack tilts
8.
Solid A is a box 4 by 3 by 10 cm. Solid B is 10 cm tall with curved sides, and every slice has area 12 cm². Ren compares them. What is true?
- A is 120 cm³, but B cannot be found without its shape
- A is larger: a box looks bulkier
- B is larger: its curved surface is longer than the box's surface
- Equal, 120 cm³ each, since every slice has the same area
9.
A cone and a pyramid both have base area 30 cm² and height 12 cm. Tala compares their volumes. What is true?
- The cone is larger because its base is round
- They are equal: (1/3) × 30 × 12 = 120 cm³ each
- The cone is (1/3)π × 30² × 12 ≈ 11,310 cm³, using the area as the radius
- Both are 360 cm³: base area times height
10.
Sketch, not to scale. A sphere has radius 5 cm. A flat cut 3 cm from its center makes a circle. Zee finds the circle's area. What is it?
- 16π cm²: radius √(5² − 3²) = 4
- 25π cm²: the sphere's biggest circle
- 34π cm²: radius √(5² + 3²)
- 9π cm²: radius 3

Volume of combined solids

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1.
Ari's silo is a cylinder 8 m across and 10 m tall, topped by a half-ball. Which expression gives its volume in m³?
- π·4²·10
- π·8²·10 + (2/3)π·8³
- π·4²·10 + (4/3)π·4³
- π·4²·10 + (2/3)π·4³
2.
Bo's toy rocket is a can 6 in across and 10 in tall with a cone tip 4 in tall. Which expression gives its volume in in³?
- π·3²·10 = 90π
- π·6²·10 + (1/3)π·6²·4 = 408π
- π·3²·10 + (1/3)π·3²·4 = 102π
- π·3²·10 + π·3²·4 = 126π
3.
A block is 10 cm by 8 cm by 6 cm. Esme drills a round hole 4 cm across straight through the 6 cm height. Which expression gives the volume left?
- 10·8·6 − π·2²·6 = 480 − 24π
- 10·8·6 = 480
- 10·8·6 − π·4²·6 = 480 − 96π
- 10·8·6 + π·2²·6 = 480 + 24π
4.
Jun's treat is a cone 6 cm across and 9 cm tall with a half-ball scoop of the same width on top. Which expression gives its volume?
- (1/3)π·6²·9 + (2/3)π·6³
- (1/3)π·3²·9 + (4/3)π·3³ = 63π
- (1/3)π·3²·9 + (2/3)π·3³ = 45π
- π·3²·9 + (2/3)π·3³ = 99π
5.
A tent is a box 4 m by 4 m by 2 m with a pyramid roof. Each sloping face has slant height 2.5 m. Kira finds the volume. What is it?
- 56 m³: the roof taken as 4 × 4 × 1.5
- 8 m³, the roof alone
- 45⅓ m³: roof height taken as the slant, 2.5 m
- 40 m³: roof height √(2.5² − 2²) = 1.5 m
6.
A funnel is a cone with radius 3 cm and slant height 5 cm. Luz finds the volume. What is it?
- 12π cm³: height √(5² − 3²) = 4 cm
- 4 cm: the height
- 36π cm³: π·3²·4, no third
- 15π cm³: height taken as the slant, 5 cm
7.
Sketch, not to scale. A straight stack of coins has volume 100 cm³. Pia slides the coins so the stack leans, with the same coins and the same height. What is the volume now?
- Still 100 cm³: every layer keeps the same area
- Less than 100 cm³: the leaning stack looks smaller
- More than 100 cm³: the slanted side is longer
- 100 × cos of the lean angle, because the stack tilts
8.
Solid A is a box 4 by 3 by 10 cm. Solid B is 10 cm tall with curved sides, and every slice has area 12 cm². Ren compares them. What is true?
- A is 120 cm³, but B cannot be found without its shape
- A is larger: a box looks bulkier
- B is larger: its curved surface is longer than the box's surface
- Equal, 120 cm³ each, since every slice has the same area
9.
A cone and a pyramid both have base area 30 cm² and height 12 cm. Tala compares their volumes. What is true?
- The cone is larger because its base is round
- They are equal: (1/3) × 30 × 12 = 120 cm³ each
- The cone is (1/3)π × 30² × 12 ≈ 11,310 cm³, using the area as the radius
- Both are 360 cm³: base area times height
10.
Sketch, not to scale. A sphere has radius 5 cm. A flat cut 3 cm from its center makes a circle. Zee finds the circle's area. What is it?
- 16π cm²: radius √(5² − 3²) = 4
- 25π cm²: the sphere's biggest circle
- 34π cm²: radius √(5² + 3²)
- 9π cm²: radius 3