Solid Metal Cone

00:00 7 marks

A solid metal cone has a base radius of 8 cm and a height of 15 cm.

(a) Calculate the volume of the cone. [2]
(b) Calculate the slant height of the cone. [2]
(c) Calculate the total surface area of the cone. [3]

Part a

3 minutes 2 marks

Question

Calculate the volume of the cone.

Hint Hint

Hint

Use the formula \(V = \frac{1}{3}\pi r^2 h\) with \(r = 8\) cm and \(h = 15\) cm.

Answer Answer
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\(V = \frac{1}{3}\pi (8^2)(15) = 320\pi\;\text{cm}^3 \approx 1010\;\text{cm}^3\)

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Part b

2 minutes 2 marks

Question

Calculate the slant height of the cone.

Hint Hint

Hint

Use the Pythagorean theorem: \(l = \sqrt{r^2+h^2}\).

Answer Answer
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Explanation Explanation

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Complete Answer

\(l = \sqrt{8^2+15^2} = \sqrt{64+225} = \sqrt{289} = 17\;cm\)

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Part c

3 minutes 3 marks

Question

Calculate the total surface area of the cone.

Hint Hint

Hint

Recall that the total surface area is the sum of the base area and the lateral surface area: \(A = \pi r^2 + \pi r l\).

Answer Answer
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Explanation Explanation

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Complete Answer

\(A = \pi(8^2) + \pi(8)(17) = 64\pi + 136\pi = 200\pi\;cm^2 \approx 628\;cm^2\)

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Solid Metal Cone

Part a

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Part b

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Part c

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Solid Metal Cone

Part a

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Part b

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Part c

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