KnowledgeBoat Logo

Mathematics

A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.

Mensuration

4 Likes

Answer

Given,

Height of the cone (h) = 15 cm

Diameter of the cone = 7 cm

A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed. Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

Radius of cone (r) = 72\dfrac{7}{2} = 3.5 cm

So, radius of the hemisphere (R) = 3.5 cm

From figure,

Volume of the solid (V) = Volume of the cone + Volume of the hemisphere

V=13πr2h+23πR3=13×227×(3.5)2×15+23×227×(3.5)3=13×227×12.25×15+23×227×42.875=22×1.75×5+1886.521=192.5+89.833=282.33 cm3.V = \dfrac{1}{3}πr^2h + \dfrac{2}{3}πR^3 \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times (3.5)^2 \times 15 + \dfrac{2}{3} \times \dfrac{22}{7} \times (3.5)^3 \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times 12.25 \times 15 + \dfrac{2}{3} \times \dfrac{22}{7} \times 42.875 \\[1em] = 22 \times 1.75 \times 5 + \dfrac{1886.5}{21} \\[1em] = 192.5 + 89.833 \\[1em] = 282.33\text{ cm}^3.

Hence, volume of solid formed = 282.33 cm3.

Answered By

2 Likes

Related Questions