An ice-cream cone is filled completely and topped with a hemisphere of ice cream. The cone has radius 7 cm and height 10 cm, and the hemisphere has the same radius. What is the total volume of ice cream? Take $\pi = \frac{22}{7}$ .

1,232 cm³Correct answerYour answer1,540 cm³Correct answerYour answer

1{,}950\frac{2}{3}

cm³Correct answerYour answer

2{,}258\frac{2}{3}

cm³Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Cone = $\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 10 = \frac{1540}{3}$ cm³.
Hemisphere = $\frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 = \frac{2156}{3}$ cm³.
Total = $\frac{3696}{3} = 1232$ cm³.

Worth noting

2,258⅔ cm³ treats the cone as a cylinder (forgetting the ⅓), and 1,540 cm³ is that cylinder with the hemisphere left out. 1,950⅔ cm³ tops the cone with a full sphere instead of a hemisphere.

Concept: Volume of a combined solid
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsMelting, recasting and combined solids

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Ten questions from Mensuration: Areas and Volumes, at your own pace.

An ice-cream cone is filled completely and topped with a hemisphere of ice cream. The cone has radius 7 cm and height 10 cm, and the hemisphere has the same radius. What is the total volume of ice cream? Take π=227\pi = \frac{22}{7}π=722​.

Explanation

An ice-cream cone is filled completely and topped with a hemisphere of ice cream. The cone has radius 7 cm and height 10 cm, and the hemisphere has the same radius. What is the total volume of ice cream? Take $\pi = \frac{22}{7}$ .