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Surface Areas and Volumes
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10
Question:
[Section C]
A wooden toy rocket is in the shape of a cone mounted on a hemisphere. The radius of the hemisphere is $3.5$ cm and the total height of the rocket is $5$ cm. Find the area to be colored if the entire surface is to be painted. (Take $\pi = 22/7$).
A wooden toy rocket is in the shape of a cone mounted on a hemisphere. The radius of the hemisphere is $3.5$ cm and the total height of the rocket is $5$ cm. Find the area to be colored if the entire surface is to be painted. (Take $\pi = 22/7$).
Step-by-Step Solution
Key Concept: Radius $r = 7/4$ cm, Cone height $h = 5 - 7/4 = 13/4$ cm. Slant height $l = \sqrt{r^2 + h^2}$. Total Area $= 2\pi r^2 + \pi r l$.
Cone slant height $l = \sqrt{(7/4)^2 + (13/4)^2} = \dfrac{\sqrt{218}}{4}$ cm. [1.0 Mark]
Area to color $= \text{CSA Hemisphere} + \text{CSA Cone} = 2\pi r^2 + \pi r l$. [1.0 Mark]
$= 2\left(\dfrac{22}{7}\right)\left(\dfrac{7}{4}\right)^2 + \left(\dfrac{22}{7}\right)\left(\dfrac{7}{4}\right)\left(\dfrac{\sqrt{218}}{4}\right) \approx 39.46$ cm$^2$. [1.0 Mark]
Area to color $= \text{CSA Hemisphere} + \text{CSA Cone} = 2\pi r^2 + \pi r l$. [1.0 Mark]
$= 2\left(\dfrac{22}{7}\right)\left(\dfrac{7}{4}\right)^2 + \left(\dfrac{22}{7}\right)\left(\dfrac{7}{4}\right)\left(\dfrac{\sqrt{218}}{4}\right) \approx 39.46$ cm$^2$. [1.0 Mark]
Correct Answer: Total Area $= 39.46$ cm$^2$
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