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Class 10 › Mathematics › Surface Areas and Volumes
CBSE2026Class Class 10 · Mathematics4 Marks · Long✅ Verified
There are many varieties of mushrooms available in the world. One such mushroom 'Amanita muscaria' has an upper part like a red cap (hemispherical) and a lower part like a white stem (cylindrical). The hemispherical cap's radius = 3 cm and the cylindrical stem is 2 cm high with diameter 1.4 cm. Considering the mushroom a solid object, answer the following questions:
(i) What is the total height of a mushroom?
(ii) Find the volume of the stem.
(iii)(a) Determine the volume of 7 such mushrooms.
OR
(iii)(b) Find the total surface area of 7 such mushrooms.
✅ Answer & Solution
Hemispherical cap: radius $R=3$ cm. Cylindrical stem: radius $r=0.7$ cm, height $h=2$ cm.
(i) $$\text{Total height}=R+h=3+2=5\ cm$$
(ii) $$V(\text{stem})=\pi r^2h=\frac{22}{7}\times0.49\times2=3.08\ cm^3$$
(iii)(a) $$V(\text{cap, hemisphere})=\frac23\pi R^3=\frac23\times\frac{22}{7}\times27=\frac{396}{7}\approx56.57\ cm^3$$ One mushroom's volume $\approx56.57+3.08=59.65\ cm^3$. For 7 mushrooms: $$7\times59.65\approx417.55\ cm^3$$
OR
(iii)(b) Surface area of one mushroom (CSA of hemisphere + CSA of cylinder + base circle of cylinder):
$$CSA(\text{hemisphere})=2\pi R^2=2\times\frac{22}{7}\times9\approx56.57\ cm^2$$ $$CSA(\text{cylinder})=2\pi rh=2\times\frac{22}{7}\times0.7\times2\approx8.8\ cm^2$$ $$\text{Base circle}=\pi r^2=\frac{22}{7}\times0.49\approx1.54\ cm^2$$ One mushroom $\approx56.57+8.8+1.54=66.91\ cm^2$. For 7 mushrooms: $$7\times66.91\approx468.37\ cm^2$$
