For a frustum with end radii 19 cm and 3 cm and a height of 21 cm, a student computed its volume as 1/3\π h (R - r)^2 instead of 1/3\π h (R^2 + r^2 + Rr) . By how many cm³ does the student’s answer fall short of the true volume? (Take \π = 22/7 .)

Question

Accepted Answer

3762. True volume = 1/3 × 22/7 × 21 × (361 + 9 + 57) = 22 × 427 = 9394 cm³. The student used (19 - 3)^2 = 256 , giving 22 × 256 = 5632 cm³. Shortfall = 9394 - 5632 = 3762 cm³. 5632 is the student’s own wrong volume; 9394 is the true volume, not the shortfall; 15026 adds the two instead of subtracting.

For a frustum with end radii 19 cm and 3 cm and a height of 21 cm, a student computed its volume as $\frac{1}{3} πh (R - r)^{2}$ instead of $\frac{1}{3} πh (R^{2} + r^{2} + R r)$ . By how many $cm^{3}$ does the student’s answer fall short of the true volume? (Take $π = \frac{22}{7} .$ )

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More Class 10 Frustum of a Cone practice

For a frustum with end radii 19 cm and 3 cm and a height of 21 cm, a student computed its volume as 31​πh(R−r)2 instead of 31​πh(R2+r2+Rr). By how many cm3 does the student’s answer fall short of the true volume? (Take π=722​.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Frustum of a Cone practice

For a frustum with end radii 19 cm and 3 cm and a height of 21 cm, a student computed its volume as $\frac{1}{3} πh (R - r)^{2}$ instead of $\frac{1}{3} πh (R^{2} + r^{2} + R r)$ . By how many $cm^{3}$ does the student’s answer fall short of the true volume? (Take $π = \frac{22}{7} .$ )