If the area of the base of a right circular cone is 51cm² and it's volume is 85cm², then the height of the cone is given as (A) 5/6 cm (B) 5/3 cm (C) 5/2 cm (D) 5cm

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 11

From the official CBSE sample question paper for 2025-26, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQSurface Areas and Volumes

If the area of the base of a right circular cone is 51cm $^{2}$ and it's volume is 85cm $^{2}$ , then the height of the cone is given as

(A) $\frac{5}{6}$ cm
(B) $\frac{5}{3}$ cm
(C) $\frac{5}{2}$ cm
(D)5cm

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

The base area is $π r^{2}$ ; you do not need to find r.

Hint 2

Substitute the base area directly into $V = \frac{1}{3} π r^{2} h$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$V = \frac{1}{3} \times (base area) \times h$ , so $85 = \frac{1}{3} \times 51 \times h$ .
$h = \frac{3 \times 85}{51} = 5$ cm. The answer is option (D). (The volume should be read as 85 cm $^{3}$ .)
1 mark

Answer: h = 5 cm, option (D)

Where the marks are

Uses $V = \frac{1}{3} π r^{2} h$ with $π r^{2} = 51$ and gets h = 5 cm, option (D) (1 mark)

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Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 11

Hints

Step-by-step solution

Revise the chapter

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