From a solid cylinder of radius 7 cm and height 24 cm, a cone of the same radius and height is hollowed out, with its base on the top face of the cylinder. What is the total surface area of the solid that remains? Take $\pi = \frac{22}{7}$ .

1,210 cm²Correct answerYour answer1,738 cm²Correct answerYour answer1,760 cm²Correct answerYour answer1,914 cm²Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Outside wall = $2 \times \frac{22}{7} \times 7 \times 24 = 1056$ cm². Bottom face = $\frac{22}{7} \times 49 = 154$ cm².
The top face is now the cone's opening, so it is gone. Inside, the cone's curved surface shows: slant $\sqrt{7^2 + 24^2} = 25$ , area $22 \times 25 = 550$ cm².
Total = $1{,}056 + 154 + 550 = 1{,}760$ cm².

Worth noting

1,914 cm² keeps the top face, which has been cut away. 1,210 cm² forgets the new inner surface, and 1,738 cm² uses the height instead of the slant height for it.

Concept: Surface area after hollowing out a cone
Typical timeTypical: 115 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.

From a solid cylinder of radius 7 cm and height 24 cm, a cone of the same radius and height is hollowed out, with its base on the top face of the cylinder. What is the total surface area of the solid that remains? Take π=227\pi = \frac{22}{7}π=722​.

Explanation

From a solid cylinder of radius 7 cm and height 24 cm, a cone of the same radius and height is hollowed out, with its base on the top face of the cylinder. What is the total surface area of the solid that remains? Take $\pi = \frac{22}{7}$ .