The curved surface of a cone is 4,070 cm² and the diameter of its base is 70 cm. What is its volume? Take $\pi = \frac{22}{7}$ .

7,700 cm³Correct answerYour answer15,400 cm³Correct answerYour answer46,200 cm³Correct answerYour answer61,600 cm³Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Radius = 35 cm. $\pi r l = 4070$ gives $l = 4070 \div 110 = 37$ cm.
Height = $\sqrt{37^2 - 35^2} = \sqrt{144} = 12$ cm.
Volume = $\frac{1}{3} \times \frac{22}{7} \times 35 \times 35 \times 12 = 15{,}400$ cm³.

Worth noting

46,200 cm³ forgets the ⅓, and 61,600 cm³ uses 70 cm as the radius. The height is not the slant height: find it by Pythagoras.

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

The curved surface of a cone is 4,070 cm² and the diameter of its base is 70 cm. What is its volume? Take π=227\pi = \frac{22}{7}π=722​.